\(A=\dfrac{3}{x+2} B=\dfrac{-11}{2x-3} C=\dfrac{x+3}{x+1}D=\dfrac{2x+10}{x+3}\)
giúp mik với mn nếu ai trả lời đc thì cho mik cảm ơn nha
Mik đg cần
giúp mik 3 câu này với
a) \(\dfrac{10}{x+2}\);\(\dfrac{5}{2x-4}\);\(\dfrac{1}{6-3x}\)
b) \(\dfrac{1}{x+2}\);\(\dfrac{8}{2x-x^2}\)
c) \(\dfrac{4x^2-3x+5}{x^3-1}\);\(\dfrac{1-2x}{x^2+x+1}\);-2
Xin cảm ơn vì các bạn đã giúp mình
Lời giải:
a.
\(\frac{10}{x+2}=\frac{60}{6(x+2)}=\frac{60(x-2)}{6(x+2)(x-2)}=\frac{60(x-2)}{6(x^2-4)}\)
\(\frac{5}{2x-4}=\frac{15(x+2)}{6(x-2)(x+2)}=\frac{15(x+2)}{6(x^2-4)}\)
\(\frac{1}{6-3x}=\frac{x+2}{3(2-x)}=\frac{2(x+2)^2}{6(2-x)(2+x)}=\frac{-2(x+2)^2}{6(x^2-4)}\)
b.
\(\frac{1}{x+2}=\frac{x(2-x)}{x(x+2)(2-x)}=\frac{x(2-x)}{x(4-x^2)}\)
\(\frac{8}{2x-x^2}=\frac{8(x+2)}{(x+2)x(2-x)}=\frac{8(x+2)}{x(4-x^2)}\)
c.
\(\frac{4x^2-3x+5}{x^3-1}\)
\(\frac{1-2x}{x^2+x+1}=\frac{(1-2x)(x-1)}{(x-1)(x^2+x+1)}=\frac{-2x^2+3x-1}{x^3-1}\)
\(-2=\frac{-2(x^3-1)}{x^3-1}\)
Giaỉ các bất phương trình sau rồi biểu diễn tập nghiệm trên trục số
d)\(\dfrac{2x+1}{3}-\dfrac{1-x}{2}\) ≥\(1-\dfrac{x}{4}\)
e) \(\dfrac{x+1}{2}-\dfrac{2-x}{3}< \dfrac{2x-3}{4}\)
GIÚP MIK NHA MN
d: Ta có: \(\dfrac{2x+1}{3}-\dfrac{1-x}{2}\ge1-\dfrac{x}{4}\)
\(\Leftrightarrow8x+4-6+6x\ge12-3x\)
\(\Leftrightarrow14x+3x\ge12+2=14\)
\(\Leftrightarrow x\ge\dfrac{14}{17}\)
e: Ta có: \(\dfrac{x+1}{2}-\dfrac{2-x}{3}< \dfrac{2x-3}{4}\)
\(\Leftrightarrow6x+12+4x-8< 6x-9\)
\(\Leftrightarrow4x< -9+8-12=-13\)
hay \(x< -\dfrac{13}{4}\)
\(P=\left(\dfrac{3+x}{3-x}-\dfrac{3-x}{3+x}+\dfrac{4x^2}{x^2-9}\right):\left(\dfrac{2x+1}{x+3}-1\right)\)
jup mik với mik cần gấp tính P=? nha
`P=((3+x)/(3-x)-(3-x)/(3+x)+(4x^2)/(x^2-9)):((2x+1)/(x+3)-1)`
`=((4x^2-(3-x)^2-(3+x)^2)/(x^2-9)):((2x+1-x-3)/(x+3))`
`=((4x^2-x^2+6x-9-x^2-6x-9)/(x^2-9)):((x-2)/(x+3))`
`=((2x^2-18)/(x^2-9))*(x+3)/(x-2)`
`=((2(x^2-9))/(x^2-9))*(x+3)/(x-2)`
`=(2x+6)/(x-2)`
ĐKXĐ: \(x\ne\pm3;x\ne-\dfrac{1}{2};x\ne2\)
\(P=\left(\dfrac{3+x}{3-x}-\dfrac{3-x}{3+x}-\dfrac{4x^2}{\left(3-x\right)\left(3+x\right)}\right):\dfrac{2x+1-x-3}{x+3}\)
\(=\dfrac{\left(3+x\right)^2-\left(3-x\right)^2-4x^2}{\left(3+x\right)\left(3-x\right)}:\dfrac{x-2}{x+3}\)
\(=\dfrac{\left(3+x-3+x\right)\left(3+x+3-x\right)-4x^2}{\left(x+3\right)\left(3-x\right)}.\dfrac{x+3}{x-2}\)
\(=\dfrac{12x-4x^2}{3-x}\cdot\dfrac{1}{x-2}\)
\(=\dfrac{4x\left(3-x\right)}{3-x}\cdot\dfrac{1}{x-2}\) \(=\dfrac{4x}{x-2}\)
Chắc mình làm tắt quá để mình làm lại bước biến đổi.
`P=((3+x)/(3-x)-(3-x)/(3+x)+(4x^2)/(x^2-9)):((2x+1)/(x+3)-1)`
`=((x-3)/(x+3)+(4x^2)/(x^2-9)-(x+3)/(x-3)):((2x+1-x-3)/(x+3))`
`=((x-3)^2/(x^2-9)+(4x^2)/(x^2-9)-(x+3)^2/(x^2-9)):((x-2)/(x+3))`
`=(((x-3)^2+4x^2-(x+3)^2)/(x^2-9))*(x+3)/(x-2)`
`=(x^2-6x+9+4x^2-x^2-6x-9)/(x^2-9)*(x+3)/(x-2)`
`=(4x^2-12x)/(x^2-9)*(x+3)/(x-2)`
`=(4x(x-3))/((x-3)(x+3))*(x+3)/(x-2)`
`=(4x)/(x+3)*(x+3)/(x-2)`
`=(4x)/(x-2)`
Tìm x :
c) \(\dfrac{x+4}{20}=\dfrac{5}{x+4}\) d) \(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\)
mọi người ơi giúp mik với , ai làm đc mik tick cho
c) \(\dfrac{x+4}{20}=\dfrac{5}{x+4}\)
⇔\(\left(x+4\right)\left(x+4\right)=100\)
⇔\(\left(x+4\right)^2=10^2\)
⇔\(\left[{}\begin{matrix}x+4=10\\x+4=-10\end{matrix}\right.\)
⇔\(\left[{}\begin{matrix}x=6\\x=-14\end{matrix}\right.\)
\(c,ĐK:x\ne-4\\ PT\Leftrightarrow\left(x+4\right)^2=100\\ \Leftrightarrow\left[{}\begin{matrix}x+4=10\\x+4=-10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\left(tm\right)\\x=-14\left(tm\right)\end{matrix}\right.\\ d,ĐK:x\ne-2;x\ne-3\\ PT\Leftrightarrow\left(x-1\right)\left(x+3\right)=\left(x-2\right)\left(x+2\right)\\ \Leftrightarrow x^2+2x-3=x^2-4\\ \Leftrightarrow2x=-1\Leftrightarrow x=-\dfrac{1}{2}\left(tm\right)\)
Cho biểu thức sau
\(A=\dfrac{x-3}{x+2}vàB=\dfrac{6-7x}{x^2-4}+\dfrac{3}{x+2}-\dfrac{2}{2-x}\)
a) Cho A=\(\dfrac{1}{2}\), khi đó hãy tính giá trị của B
GIÚP MIK nha mn mik đang cần gấp =(((
a: Ta có: \(A=\dfrac{1}{2}\)
\(\Leftrightarrow x+2=2x-6\)
\(\Leftrightarrow-x=-8\)
hay x=8
Thay x=8 vào B,ta được:
\(B=-\dfrac{2}{8+2}=-\dfrac{2}{10}=-\dfrac{1}{5}\)
cho bt A = \(\dfrac{x^2+x}{x^2-2x+1}:\left(\dfrac{x+1}{x}-\dfrac{1}{1-x}+\dfrac{2-x^2}{x^2-x}\right)\)
a) tìm đkxđ và rút gọn A
b) tìm x để A = \(\dfrac{-1}{2}\)
c) tìm x để A<1
d) tìm x nguyên để A nguyên
Mik đang cần gấp, mik cảm ơn!!!
\(A=\dfrac{x^2+x}{x^2-2x+1}:\left(\dfrac{x+1}{x}-\dfrac{1}{1-x}+\dfrac{2-x^2}{x^2-x}\right)\left(1\right)\)
a) A xác định \(\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne1\end{matrix}\right.\)
\(\left(1\right)\Rightarrow A=\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\dfrac{x+1}{x}+\dfrac{1}{x-1}+\dfrac{2-x^2}{x\left(x-1\right)}\right)\)
\(\Rightarrow A=\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\dfrac{\left(x+1\right)\left(x-1\right)+x+2-x^2}{x\left(x-1\right)}\right)\)
\(\Rightarrow A=\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\dfrac{x^2-1+x+2-x^2}{x\left(x-1\right)}\right)\)
\(\Rightarrow A=\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\dfrac{x+1}{x\left(x-1\right)}\right)\)
\(\Rightarrow A=\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}.\dfrac{x\left(x-1\right)}{x+1}=\dfrac{x^2}{x+1}\)
b) Để \(A=-\dfrac{1}{2}\)
\(\Leftrightarrow\dfrac{x^2}{x+1}=-\dfrac{1}{2}\left(x\ne-1\right)\)
\(\Leftrightarrow2x^2=-\left(x+1\right)\)
\(\Leftrightarrow2x^2+x+1=0\)
\(\Delta=1-8=-7< 0\)
Nên phương trình trên vô nghiệm \(\left(x\in\varnothing\right)\)
c) Để \(A< 1\)
\(\Leftrightarrow\dfrac{x^2}{x+1}< 1\)
\(\Leftrightarrow x^2< x+1\left(x\ne-1\right)\)
\(\Leftrightarrow x^2-x-1< 0\)
\(\Leftrightarrow x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-1< 0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2-\dfrac{5}{4}< 0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2< \dfrac{5}{4}\)
\(\Leftrightarrow-\dfrac{\sqrt[]{5}}{2}< x-\dfrac{1}{2}< \dfrac{\sqrt[]{5}}{2}\)
\(\Leftrightarrow\dfrac{-\sqrt[]{5}+1}{2}< x< \dfrac{\sqrt[]{5}+1}{2}\)
d) Để A nguyên
\(\Leftrightarrow\dfrac{x^2}{x+1}\in Z\)
\(\Leftrightarrow x^2⋮x+1\)
\(\Leftrightarrow x^2-x\left(x+1\right)⋮x+1\)
\(\Leftrightarrow x^2-x^2+x⋮x+1\)
\(\Leftrightarrow x⋮x+1\)
\(\Leftrightarrow x-x-1⋮x+1\)
\(\Leftrightarrow-1⋮x+1\)
\(\Leftrightarrow x+1\in\left\{-1;1\right\}\)
\(\Leftrightarrow x\in\left\{-2;0\right\}\left(x\in Z\right)\)
Bài 3 : Tính
a) \(\dfrac{2}{5}+\dfrac{11}{15}\) b) \(\dfrac{2}{7}-\dfrac{2}{11}\) c) \(\dfrac{11}{13}\) x \(\dfrac{26}{31}\) d) \(\dfrac{1}{2}:\dfrac{1}{3}\) x \(\dfrac{2}{5}\)
giúp mik với , giải rõ ràng ra nha . ( đùưng vào nói ltinh gì zới mik nha )
a \(\dfrac{6}{15}+\dfrac{11}{15}=\dfrac{17}{15}\)
b \(\dfrac{22}{77}-\dfrac{14}{77}=\dfrac{8}{77}\)
c \(\dfrac{11}{13}\times\dfrac{26}{31}=11\times\dfrac{2}{31}=\dfrac{22}{31}\)
d \(\dfrac{1}{2}\times3\times\dfrac{2}{5}=\dfrac{3}{5}\)
a, 2/5 + 11/15 = 6/15 + 11/15 = 17/15
b,2/7 - 2/11 = 22/77 - 14/77 = 8/77
c, 11/13 x 26/31= 11 x 2/31 =22/31
d, 1/2 : 1/3 x 2/5
= ( 1/2 x 2/5 ) : 1/3
= 1/5 : 1/3
= 3/5
a/ \(\dfrac{-3}{5}\) - x = \(\dfrac{21}{10}\)
b/ x : \(\dfrac{2}{9}\) = \(\dfrac{9}{2}\)
c/ \(\dfrac{x}{9}\) = \(\dfrac{5}{3}\)
d/ x : \(\left(\dfrac{2}{5}\right)^3\)= \(\left(\dfrac{5}{2}\right)^3\)
giúp mik gấp nha, mik sắp thi rồi!
\(\dfrac{-3}{5}-x=\dfrac{21}{10}\)
\(x=\dfrac{-3}{5}-\dfrac{21}{10}\)
\(x=\)-\(\dfrac{27}{10}\)
\(x:\dfrac{2}{9}=\dfrac{9}{2}\)
\(x.\dfrac{9}{2}=\dfrac{9}{2}\)
\(x=\dfrac{9}{2}:\dfrac{9}{2}\)
\(x=1\)
\(\dfrac{x}{9}=\dfrac{5}{3}\)
\(x.3=5.9\)
\(x.3=45\)
\(x=45:3=15\)
\(x:\left(\dfrac{2}{5}\right)^3=\left(\dfrac{5}{2}\right)^3\)
\(x:\dfrac{8}{125}=\dfrac{125}{8}\)
\(x.\dfrac{125}{8}=\dfrac{125}{8}\)
\(x=\dfrac{125}{8}:\dfrac{125}{8}=1\)
Cho 2 phân thức A=\(\dfrac{2x^2+20}{x^2-4}+\dfrac{3}{x+2}-\dfrac{7}{x-2}\) và B=\(\dfrac{2x^2}{3x+6}\) (x≠2, x≠-2, x≠0)
a, Tính B khi x=-3
b, Rút gọn phân thức A
"giúp e với ạ e đg cần gấp, cảm ơn ạ"
a: Thay x=-3 vào B, ta được:
\(B=\dfrac{2\cdot\left(-3\right)^2}{3\cdot\left(-3\right)+6}=\dfrac{2\cdot9}{-9+6}=\dfrac{18}{-3}=-6\)
b: \(A=\dfrac{2x^2+20+3x-6-7x-14}{\left(x+2\right)\left(x-2\right)}=\dfrac{2x^2-4x}{\left(x+2\right)\left(x-2\right)}=\dfrac{2x}{x+2}\)