Solve 5/x^2+2x-3=1/x+3-28/x-1

$$\frac { 5 } { x ^ { 2 } + 2 x - 3 } = \frac { 1 } { x + 3 } - \frac { 28 } { x - 1 }$$

Solve for x

$$x = -\frac{10}{3} = -3\frac{1}{3} \approx -3.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+3\right), the least common multiple of x^{2}+2x-3,x+3,x-1.

$$5=x-1-\left(x+3\right)\times 28$$

Use the distributive property to multiply x+3 by 28.

$$5=x-1-\left(28x+84\right)$$

To find the opposite of 28x+84, find the opposite of each term.

$$5=x-1-28x-84$$

Combine x and -28x to get -27x.

$$5=-27x-1-84$$

Subtract 84 from -1 to get -85.

$$5=-27x-85$$

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

$$-27x-85=5$$

Add 85 to both sides.

$$-27x=5+85$$

Add 5 and 85 to get 90.

$$-27x=90$$

Divide both sides by -27.

$$x=\frac{90}{-27}$$

Reduce the fraction \frac{90}{-27} to lowest terms by extracting and canceling out 9.

$$x=-\frac{10}{3}$$