Tính :
a) \(\left(-30\right)+\left(-5\right)\)
b) \(\left(-7\right)+\left(-13\right)\)
c) \(\left(-15\right)+\left(-235\right)\)
a) A=\(\left(\frac{-5}{11}\right).\frac{7}{15}.\left(\frac{11}{-5}\right).\left(-30\right)\)
b) B=\(\left(-\frac{1}{6}\right).\left(\frac{-15}{19}\right).\left(\frac{38}{45}\right)\)
c) C= \(\left(\frac{-5}{9}\right).\frac{3}{11}+\left(\frac{-13}{18}\right).\frac{3}{11}\)
d) D= \(\left(2\frac{2}{15}.\frac{9}{17}.\frac{3}{32}\right):\left(\frac{-3}{27}\right)\)
Áp dụng tính chất \(a\left(b-c\right)=ab-ac\) , điền số thích hợp vào chỗ trống :
a) \(.......\left(-13\right)+8.\left(-13\right)=\left(-7+8\right).\left(-13\right)=.......\)
b) \(\left(-5\right)\left(-4-......\right)=\left(-5\right).\left(-4\right)-\left(-5\right).\left(-14\right)=.......\)
hãy tính giá trị của biểu thức sau:
C=\(\left|-3\left(-\dfrac{13}{15}-\dfrac{17}{21}\right)\right|-\left|-\dfrac{13}{5}+\dfrac{17}{7}\right|+\left(-12+\dfrac{35}{3}\right):\left|-\dfrac{7}{6}\right|\)
\(C=\left|-3\left(\dfrac{-13}{15}-\dfrac{17}{21}\right)\right|-\left|\dfrac{-13}{15}+\dfrac{17}{7}\right|+\left(-12+\dfrac{35}{3}\right):\left|-\dfrac{7}{6}\right|\\ =\left|-3.-\dfrac{176}{105}\right|-\left|-\dfrac{6}{35}\right|+\left(-\dfrac{1}{3}\right):\dfrac{7}{6}\\ =\dfrac{176}{35}-\dfrac{6}{35}-\dfrac{1}{3}:\dfrac{7}{6}\\ =\dfrac{176}{35}-\dfrac{6}{35}-\dfrac{2}{7}\\ =\dfrac{170}{35}-\dfrac{2}{7}=\dfrac{32}{7}.\)
Tính :
a) \(5+\left(-7\right)+9+\left(-11\right)+13+\left(-15\right)\)
b) \(\left(-6\right)+8+\left(-10\right)+12+\left(-14\right)+16\)
a)
\(5+\left(-7\right)+9+\left(-11\right)+13+\left(-15\right)\)
\(=\left[5+\left(-7\right)\right]+\left[9+\left(-11\right)\right]+\left[13+\left(-15\right)\right]\)
\(=\left(-2\right)+\left(-2\right)+\left(-2\right)=-6\)
b)
\(\left(-6\right)+8+\left(-10\right)+12+\left(-14\right)+16\)
\(=\left[\left(-6\right)+8\right]+\left[\left(-10\right)+12\right]+\left[\left(-14\right)+16\right]\)
\(=2+2+2=6\)
tìm x biết:
A) \(\frac{7}{\left(x+3\right)\left(x+10\right)}\)\(+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
B)\(\frac{3}{\left(x-4\right)\left(x-7\right)}+\frac{6}{\left(x-7\right)\left(x-13\right)}+\frac{15}{\left(x-13\right)\left(x-28\right)}-\frac{1}{x-28}=-\frac{5}{2}\)
A) \(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}\)
\(=\frac{\left(x+10\right)-\left(x+3\right)}{\left(x+3\right)\left(x+10\right)}+\frac{\left(x+21\right)-\left(x+10\right)}{\left(x+10\right)\left(x+21\right)}+\frac{\left(x+34\right)-\left(x+21\right)}{\left(x+21\right)\left(x+34\right)}\)
\(=\frac{1}{x+3}-\frac{1}{x+10}+\frac{1}{x+10}-\frac{1}{x+21}+\frac{1}{x+21}-\frac{1}{x+34}\)
\(=\frac{1}{x+3}-\frac{1}{x+34}\)
\(=\frac{\left(x+34\right)-\left(x+3\right)}{\left(x+3\right)\left(x+34\right)}\)\(=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
\(\Rightarrow\left(x+34\right)-\left(x+3\right)=x\)
\(\Rightarrow x=31\)
Vậy, x = 31
Bạn áp dụng: \(\frac{k}{x\cdot\left(x+k\right)}=\frac{1}{x}-\frac{1}{x+k}\) với \(x,k\inℝ;x\ne0;x\ne-k\)
Chứng minh: \(\frac{1}{x}-\frac{1}{x+k}=\frac{x+k}{x\left(x+k\right)}-\frac{x}{x\left(x+k\right)}=\frac{x+k-x}{x\left(x+k\right)}=\frac{k}{x\left(x+k\right)}\)
B) \(\frac{\left(x-4\right)-\left(x-7\right)}{\left(x-7\right)\left(x-4\right)}+\frac{\left(x-7\right)-\left(x-13\right)}{\left(x-13\right)\left(x-7\right)}+\frac{\left(x-13\right)-\left(x-28\right)}{\left(x-28\right)\left(x-13\right)}\)
\(=\frac{1}{x-7}-\frac{1}{x-4}+\frac{1}{x-13}-\frac{1}{x-7}+\frac{1}{x-28}-\frac{1}{x-13}\)
\(=\frac{1}{x-28}-\frac{1}{x-4}=-\frac{5}{2}+\frac{1}{x-28}\)
\(\Leftrightarrow\frac{1}{x-28}-\frac{1}{x-4}-\frac{1}{x-28}=-\frac{5}{2}\)
\(\Leftrightarrow\frac{1}{x-4}=\frac{5}{2}\)
=> 5x - 20 = 2
=> 5x = 22
\(\Rightarrow x=\frac{22}{5}=4,4\)
Vậy, x = 4,4
Tính a)
\(A=\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}\)
b) \(M=\left(x-4\right)^{\left(x-5\right)^{\left(x-6\right)^{\left(x+6\right)^{\left(x+5\right)}}}}với x=7\)
\(A=\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}\)
\(=\frac{2^3\left(2^{27}.5^7+2^{10}.5^{27}\right)}{2^{27}.5^7+2^{10}.5^{27}}\)
\(=2^3=8\)
\(\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}+\frac{2^{13}.5^7\left(2^{17}+5^{20}\right)}{2^{10}.5^7\left(2^{17}+5^{20}\right)}=2^3=8\)
Tính bằng cách hợp lí :
\(A=\left(-5,85\right)+\left\{\left[\left(+41,3\right)+\left(+5\right)\right]+\left(+0,85\right)\right\}\)
\(B=\left(-87,5\right)+\left\{\left(+87,5\right)+\left[\left(+3,8\right)+\left(-0,8\right)\right]\right\}\)
\(C=\left[\left(+9,8\right)+\left(-13\right)\right]+\left[\left(-5\right)+\left(+8,5\right)\right]\)
\(A=\left(-5,85\right)+\left\{\left[\left(+41,3\right)+\left(+5\right)\right]+\left(+0,85\right)\right\}\)
\(A=\left(-5,85\right)+\left\{\left[41,3+5\right]+0,85\right\}\)
\(A=\left(-5,85\right)+\left\{41,3+5+0,85\right\}\)
\(A=\left(-5,85\right)+\left\{41,3+5,85\right\}\)
\(A=\left(-5,85\right)+41,3+5,85\)
\(A=\left(-5,85\right)+5,85+41,3\)
\(A=0+41,3\)
\(A=41,3\)
\(B=\left(-87,5\right)+\left\{\left(+87,5\right)+\left[\left(+3,8\right)+\left(-0,8\right)\right]\right\}\)
\(B=\left(-87,5\right)+87,5+3,8+\left(-0,8\right)\)
\(B=\left[\left(-87,5\right)+87,5\right]+\left[3,8+\left(-0,8\right)\right]\)
\(B=0+3\)
\(B=3\)
\(C=\left[\left(+9,8\right)+\left(-13\right)\right]+\left[\left(-5\right)+\left(+8,5\right)\right]\)
\(C=\left(-3,2\right)+3,5\)
\(C=0,3\)
Giải các phương trình sau:
a) \(8 - \left( {x - 15} \right) = 2.\left( {3 - 2x} \right)\);
b) \( - 6\left( {1,5 - 2u} \right) = 3\left( { - 15 + 2u} \right)\);
c) \({\left( {x + 3} \right)^2} - x\left( {x + 4} \right) = 13\);
d) \(\left( {y + 5} \right)\left( {y - 5} \right) - {\left( {y - 2} \right)^2} = 5\).
a) \(8 - \left( {x - 15} \right) = 2.\left( {3 - 2x} \right)\)
\(8 - x + 15 = 6 - 4x\)
\( - x + 4x = 6 - 8 - 15\)
\(3x = - 17\)
\(x = \left( { - 17} \right):3\)
\(x = \dfrac{{ - 17}}{3}\)
Vậy nghiệm của phương trình là \(x = \dfrac{{ - 17}}{3}\).
b) \( - 6\left( {1,5 - 2u} \right) = 3\left( { - 15 + 2u} \right)\)
\( - 9 + 12u = - 45 + 6u\)
\(12u - 6u = - 45 + 9\)
\(u = \left( { - 36} \right):6\)
\(6u = - 36\)
\(u = - 6\)
Vậy nghiệm của phương trình là \(u = - 6\).
c) \({\left( {x + 3} \right)^2} - x\left( {x + 4} \right) = 13\)
\(\left( {{x^2} + 6x + 9} \right) - \left( {{x^2} + 4x} \right) = 13\)
\({x^2} + 6x + 9 - {x^2} - 4x = 13\)
\(\left( {{x^2} - {x^2}} \right) + \left( {6x - 4x} \right) = 13 - 9\)
\(2x = 4\)
\(x = 4:2\)
\(x = 2\)
Vậy nghiệm của phương trình là \(x = 2\).
d) \(\left( {y + 5} \right)\left( {y - 5} \right) - {\left( {y - 2} \right)^2} = 5\)
\(\left( {{y^2} - 25} \right) - \left( {{y^2} - 4y + 4} \right) = 5\)
\({y^2} - 25 - {y^2} + 4y - 4 = 5\)
\(\left( {{y^2} - {y^2}} \right) + 4y = 5 + 4 + 25\)
\(4y = 34\)
\(y = 34:4\)
\(y = \dfrac{{17}}{2}\)
Vậy nghiệm của phương trình là \(y = \dfrac{{17}}{2}\).
Mình cần gấp bài này !!!
1/Tìm x, biết :
a/ \(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}+\frac{x}{\left(x+3\right)\left(x+34\right)}\)
b/ \(\frac{3}{\left(x-4\right)\left(x-7\right)}+\frac{6}{\left(x-7\right)\left(x-13\right)}+\frac{15}{\left(x-13\right)\left(x-28\right)}-\frac{1}{x-28}=\frac{-1}{20}\)