Solve 4x-8/x-5=8x/2x+5

$$\frac { 4 x - 8 } { x - 5 } = \frac { 8 x } { 2 x + 5 }$$

Solve for x

$$x=\frac{10}{11}\approx 0.909090909$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{5}{2},5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(2x+5\right), the least common multiple of x-5,2x+5.

$$\left(2x+5\right)\left(4x-8\right)=\left(x-5\right)\times 8x$$

Use the distributive property to multiply 2x+5 by 4x-8 and combine like terms.

$$8x^{2}+4x-40=\left(x-5\right)\times 8x$$

Use the distributive property to multiply x-5 by 8.

$$8x^{2}+4x-40=\left(8x-40\right)x$$

Use the distributive property to multiply 8x-40 by x.

$$8x^{2}+4x-40=8x^{2}-40x$$

Subtract 8x^{2} from both sides.

$$8x^{2}+4x-40-8x^{2}=-40x$$

Combine 8x^{2} and -8x^{2} to get 0.

$$4x-40=-40x$$

Add 40x to both sides.

$$4x-40+40x=0$$

Combine 4x and 40x to get 44x.

$$44x-40=0$$

Add 40 to both sides. Anything plus zero gives itself.

$$44x=40$$

Divide both sides by 44.

$$x=\frac{40}{44}$$

Reduce the fraction \frac{40}{44} to lowest terms by extracting and canceling out 4.

$$x=\frac{10}{11}$$