Rút gọn:
(x-2)\(^3\)-(x-3)\(^2\)
giải chi tiết giúp mình
M=(x-3)^3 - (x+1)^3 +12x(x-1)
Rút gọn M
Mn giúp mình giải chi tiết đầy đủ từng bước nhé
M = (x - 3)3 - (x + 1)3 + 12x (x - 1)
= x3 - 9x2 + 27x - 27 - (x3 + 3x2 + 3x + 1) + 12x2 - 12x
= x3 - 9x2 + 27x - 27 - x3 - 3x2 - 3x - 1 + 12x2 - 12x
= (x3 - x3) + (12x2 - 9x2 - 3x2) + (27x - 3x - 12x) - (27 + 1)
= 12x - 28
Rút gọn biểu thức sau
P=\(\dfrac{5\sqrt{x}}{\sqrt{x}-2}-\dfrac{3-\sqrt{x}}{\sqrt{x}+2}+\dfrac{6x}{4-x}\)
giải chi tiết hộ mình vs ạ
\(ĐK:x\ge0;x\ne4\\ P=\dfrac{5x+10\sqrt{x}-\left(3-\sqrt{x}\right)\left(\sqrt{x}-2\right)-6x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ P=\dfrac{5x+10\sqrt{x}-5\sqrt{x}+6+x-6x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ P=\dfrac{5\sqrt{x}+6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(P=\dfrac{5\sqrt{x}}{\sqrt{x}-2}-\dfrac{3-\sqrt{x}}{\sqrt{x}+2}+\dfrac{6x}{4-x}\left(đk:x\ge0,x\ne4\right)\)
\(=\dfrac{5\sqrt{x}\left(\sqrt{x}+2\right)-\left(3-\sqrt{x}\right)\left(\sqrt{x}-2\right)-6x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{5x+10\sqrt{x}+x-5\sqrt{x}+6-6x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{5\sqrt{x}+6}{x-4}\)
Rút gọn biểu thức sau
B=\(\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+3}{x-9}\)
giải chi tiết hộ mình vs ạ tại mới học !!!
ĐKXĐ: \(x\ge0;x\ne3\)
\(B=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\dfrac{3x+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}-3x-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{-3\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{-3\sqrt{x}-3}{x-9}\)
bỏ dấu GTTĐ và rút gọn
A = |2x-5| +3-2x
B = |x2 - 5x +4| -4+5x - x2
Giải nhanh và chi tiết giúp mình nha
A = |2x - 5| + 3 - 2x
A = 2x - 5 + 3 - 2x
A = (2x - 2x) + (-5 + 3)
A = -2
B = |x2 - 5x + 4| - 4 + 5x - x2
B = x2 - 5x + 4 - 4 + 5x - x2
B = (x2 - x2) + (-5x + 5x) + (4 - 4)
B = 0
Rút gọn biểu thức
M=\(\dfrac{3}{2}\sqrt{32x}-\dfrac{1}{3}\sqrt{18x}+\dfrac{2}{5}\sqrt{50x}-4\sqrt{2x}\) (x ≥ 0)
giải chi tiết giúp mk vớiiiiii ạ
\(M=6\sqrt{2x}-\sqrt{2x}+2\sqrt{2x}-4\sqrt{2x}=3\sqrt{2x}\)
rút gọn biểu thức sau
D=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}+1}+\dfrac{3\sqrt{x}+1}{x-1}\right):\dfrac{\sqrt{x}-2}{\sqrt{x}-1}\)
giải chi tiết hộ mình với ạ!!!
\(D=\left(\dfrac{\sqrt{x}}{\sqrt{x}+1}+\dfrac{3\sqrt{x}+1}{x-1}\right):\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\left(x\ge0;x\ne1\right)\\ D=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)+3\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}+2}\\ D=\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}+1}\cdot\dfrac{1}{\sqrt{x}+2}=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
Rút gọn biểu thức sau
P=\(\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+1:\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}-\dfrac{\sqrt{x}+1}{\sqrt{x}+2}+\dfrac{2\sqrt{x+7}}{4-x}\right)\)
giải chi tiết hộ mình vs ạ !!!
\(P=\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+1:\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}-\dfrac{\sqrt{x}+1}{\sqrt{x}+2}-\dfrac{2\sqrt{x}+7}{x-4}\right)\)
\(=\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+1:\left(\dfrac{x+2\sqrt{x}-x+\sqrt{x}+2-2\sqrt{x}-7}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right)\)
\(=\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}-5}\)
\(=\dfrac{-x+8\sqrt{x}-15+\left(x-4\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-5\right)}\)
\(=\dfrac{-x+8\sqrt{x}-15+x\sqrt{x}-2x-4\sqrt{x}+8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-5\right)}\)
\(=\dfrac{x\sqrt{x}-3x+4\sqrt{x}-7}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-5\right)}\)
\(ĐK:x\ge0;x\ne4\\ P=\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+1:\dfrac{x+2\sqrt{x}-x+\sqrt{x}+2-2\sqrt{x}-7}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ P=\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}-5}\\ P=\dfrac{\left(3-\sqrt{x}\right)\left(\sqrt{x}-5\right)+\left(x-4\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-5\right)}\\ P=\dfrac{8\sqrt{x}-15-x+x\sqrt{x}-2x-4\sqrt{x}+8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-5\right)}\\ P=\dfrac{x\sqrt{x}-3x+4\sqrt{x}-7}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-5\right)}\)
rút gọn \(\dfrac{1}{x-3}+\dfrac{3x^2-8x+10}{x^2-5x+6}-\dfrac{2x-4}{x-2}\) giải chi tiết ạ
\(\dfrac{1}{x-3}+\dfrac{3x^2-8x+10}{x^2-5x+6}-\dfrac{2x-4}{x-2}\left(ĐK:x\ne3;x\ne2\right)\)
\(=\dfrac{1}{x-3}+\dfrac{3x^2-8x+10}{x\left(x-2\right)-3\left(x-2\right)}-\dfrac{2x-4}{x-2}\)
\(=\dfrac{1}{x-3}+\dfrac{3x^2-8x+10}{\left(x-3\right)\left(x-2\right)}-\dfrac{2x-4}{x-2}\)
\(=\dfrac{x-2}{\left(x-2\right)\left(x-3\right)}+\dfrac{3x^2-8x+10}{\left(x-3\right)\left(x-2\right)}-\dfrac{\left(2x-4\right)\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{x-2+3x^2-8x+10-\left(2x^2-6x-4x+12\right)}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{3x^2-7x+8-2x^2+10x-12}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{x^2+3x-4}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{x^2+3x-4}{x^2-5x+6}\)
(x-3)^3 - (x+1)^3 + 12x(x-1)
Mn giúp mình rút gọn chi tiết đầy đủ các bước nhé
(x - 3)3 - (x + 1)3 + 12x (x - 1)
= x3 - 3x2 . 3 + 3x . 32 - 27 - (x3 + 3x2 . 1 + 3x . 12 + 13) + 12x . x + 12x . (-1)
= x3 - 9x2 + 27x - 27 - x3 - 3x2 - 3x - 1 + 12x2 - 12x
= (x3 - x3) + (12x2 - 9x2 - 3x2) + (27x - 3x - 12x) - (27 + 1)
= 12x - 28
\(\left(x-3\right)^3-\left(x+1\right)^3+12x\left(x-1\right)\)
\(\Leftrightarrow\left(x^3-3x^23+3x3^2-3^3\right)-\left(x^3+3x^21+3x1^2+1^3\right)+12x^2-12x\)
\(\Leftrightarrow x^3-9x^2+27x-27-x^3-3x^2-3x-1+12x^2-12x\)
\(\Leftrightarrow12x-28=0\)
\(\Leftrightarrow12x=28\)
\(\Leftrightarrow x=\frac{7}{3}\)
Vậy S={\(\frac{7}{3}\)} là nghiệm pt
\(\dfrac{2\sqrt{x}}{\sqrt{x}-2}\). \(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}\)
Giúp em giải chi tiết các bước rút gọn cho pt này với
\(\dfrac{2\sqrt{x}}{\sqrt{x}-2}.\dfrac{\sqrt{x}+2}{\sqrt{x}-2}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)^2}\)
\(=\dfrac{2x+4\sqrt{x}}{x-4\sqrt{x}+4}\)
\(\dfrac{2\sqrt{x}}{\sqrt{x}-2}.\dfrac{\sqrt{x}+2}{\sqrt{x}-2}=\dfrac{2\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)^2}\) (\(đk:x\ge0;x\ne\sqrt{2}\))
\(=\dfrac{2x+4\sqrt{x}}{x-4\sqrt{x}+4}\)
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