Solve 3/x-1+5/xdiv1=8x+5/x^2-1

$$\frac{ 3 }{ x-1 } + \frac{ 5 }{ x \div 1 } = \frac{ 8x+5 }{ { x }^{ 2 } -1 }$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of x-1,x^{2}-1.

$$\left(x+1\right)\times 3+\left(x-x^{-1}\right)\times 5=8x+5$$

Use the distributive property to multiply x+1 by 3.

$$3x+3+\left(x-x^{-1}\right)\times 5=8x+5$$

Use the distributive property to multiply x-x^{-1} by 5.

$$3x+3+5x-5x^{-1}=8x+5$$

Combine 3x and 5x to get 8x.

$$8x+3-5x^{-1}=8x+5$$

Subtract 8x from both sides.

$$8x+3-5x^{-1}-8x=5$$

Combine 8x and -8x to get 0.

$$3-5x^{-1}=5$$

Subtract 3 from both sides.

$$-5x^{-1}=5-3$$

Subtract 3 from 5 to get 2.

$$-5x^{-1}=2$$

Divide both sides by -5.

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

Reorder the terms.

$$\frac{1}{x}=-\frac{2}{5}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.

$$5=-2x$$

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

$$-2x=5$$

Divide both sides by -2.

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

Fraction \frac{5}{-2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

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