Solve -8/(17-8x)x=64/(8x+17)^2

$$\frac { - 8 } { ( 17 - 8 x ) x } = \frac { 64 } { ( 8 x + 17 ) ^ { 2 } }$$

Solve for x

$$x=-\frac{17}{24}\approx -0.708333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{17}{8},0,\frac{17}{8} since division by zero is not defined. Multiply both sides of the equation by x\left(8x-17\right)\left(8x+17\right)^{2}, the least common multiple of \left(17-8x\right)x,\left(8x+17\right)^{2}.

$$-\left(17+8x\right)^{2}\left(-8\right)=x\left(8x-17\right)\times 64$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(17+8x\right)^{2}.

$$-\left(289+272x+64x^{2}\right)\left(-8\right)=x\left(8x-17\right)\times 64$$

To find the opposite of 289+272x+64x^{2}, find the opposite of each term.

$$\left(-289-272x-64x^{2}\right)\left(-8\right)=x\left(8x-17\right)\times 64$$

Use the distributive property to multiply -289-272x-64x^{2} by -8.

$$2312+2176x+512x^{2}=x\left(8x-17\right)\times 64$$

Use the distributive property to multiply x by 8x-17.

$$2312+2176x+512x^{2}=\left(8x^{2}-17x\right)\times 64$$

Use the distributive property to multiply 8x^{2}-17x by 64.

$$2312+2176x+512x^{2}=512x^{2}-1088x$$

Subtract 512x^{2} from both sides.

$$2312+2176x+512x^{2}-512x^{2}=-1088x$$

Combine 512x^{2} and -512x^{2} to get 0.

$$2312+2176x=-1088x$$

Add 1088x to both sides.

$$2312+2176x+1088x=0$$

Combine 2176x and 1088x to get 3264x.

$$2312+3264x=0$$

Subtract 2312 from both sides. Anything subtracted from zero gives its negation.

$$3264x=-2312$$

Divide both sides by 3264.

$$x=\frac{-2312}{3264}$$

Reduce the fraction \frac{-2312}{3264} to lowest terms by extracting and canceling out 136.

$$x=-\frac{17}{24}$$