Solve x/x-5=x+1/x

$$\frac { x } { x - 5 } = \frac { x + 1 } { x }$$

Solve for x

$$x = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,5 since division by zero is not defined. Multiply both sides of the equation by x\left(x-5\right), the least common multiple of x-5,x.

$$xx=\left(x-5\right)\left(x+1\right)$$

Multiply x and x to get x^{2}.

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

Use the distributive property to multiply x-5 by x+1 and combine like terms.

$$x^{2}=x^{2}-4x-5$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=-4x-5$$

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

$$0=-4x-5$$

Swap sides so that all variable terms are on the left hand side.

$$-4x-5=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$-4x=5$$

Divide both sides by -4.

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

Fraction \frac{5}{-4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

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