Solve 7/x-5=x^2-10/x^2-x-20-1

$$\frac{ 7 }{ x-5 } = \frac{ { x }^{ 2 } -10 }{ { x }^{ 2 } -x-20 } -1$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+4\right), the least common multiple of x-5,x^{2}-x-20.

$$\left(x+4\right)\times 7=x^{2}-10+\left(x-5\right)\left(x+4\right)\left(-1\right)$$

Use the distributive property to multiply x+4 by 7.

$$7x+28=x^{2}-10+\left(x-5\right)\left(x+4\right)\left(-1\right)$$

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

$$7x+28=x^{2}-10+\left(x^{2}-x-20\right)\left(-1\right)$$

Use the distributive property to multiply x^{2}-x-20 by -1.

$$7x+28=x^{2}-10-x^{2}+x+20$$

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

$$7x+28=-10+x+20$$

Add -10 and 20 to get 10.

$$7x+28=10+x$$

Subtract x from both sides.

$$7x+28-x=10$$

Combine 7x and -x to get 6x.

$$6x+28=10$$

Subtract 28 from both sides.

$$6x=10-28$$

Subtract 28 from 10 to get -18.

$$6x=-18$$

Divide both sides by 6.

$$x=\frac{-18}{6}$$

Divide -18 by 6 to get -3.

$$x=-3$$