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

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

Solve for x

$$x = -\frac{44}{7} = -6\frac{2}{7} \approx -6.285714286$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+5\right), the least common multiple of x-4,x+5.

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

Use the distributive property to multiply x+5 by 4.

$$\left(4x+20\right)x-\left(x-4\right)\times 2=4\left(x-4\right)\left(x+5\right)$$

Use the distributive property to multiply 4x+20 by x.

$$4x^{2}+20x-\left(x-4\right)\times 2=4\left(x-4\right)\left(x+5\right)$$

Use the distributive property to multiply x-4 by 2.

$$4x^{2}+20x-\left(2x-8\right)=4\left(x-4\right)\left(x+5\right)$$

To find the opposite of 2x-8, find the opposite of each term.

$$4x^{2}+20x-2x+8=4\left(x-4\right)\left(x+5\right)$$

Combine 20x and -2x to get 18x.

$$4x^{2}+18x+8=4\left(x-4\right)\left(x+5\right)$$

Use the distributive property to multiply 4 by x-4.

$$4x^{2}+18x+8=\left(4x-16\right)\left(x+5\right)$$

Use the distributive property to multiply 4x-16 by x+5 and combine like terms.

$$4x^{2}+18x+8=4x^{2}+4x-80$$

Subtract 4x^{2} from both sides.

$$4x^{2}+18x+8-4x^{2}=4x-80$$

Combine 4x^{2} and -4x^{2} to get 0.

$$18x+8=4x-80$$

Subtract 4x from both sides.

$$18x+8-4x=-80$$

Combine 18x and -4x to get 14x.

$$14x+8=-80$$

Subtract 8 from both sides.

$$14x=-80-8$$

Subtract 8 from -80 to get -88.

$$14x=-88$$

Divide both sides by 14.

$$x=\frac{-88}{14}$$

Reduce the fraction \frac{-88}{14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{44}{7}$$