Solve 3/x+1+5/x-4=5/x+1

$$\frac { 3 } { x + 1 } + \frac { 5 } { x - 4 } = \frac { 5 } { x + 1 }$$

Solve for x

$$x = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+1\right), the least common multiple of x+1,x-4.

$$\left(x-4\right)\times 3+\left(x+1\right)\times 5=\left(x-4\right)\times 5$$

Use the distributive property to multiply x-4 by 3.

$$3x-12+\left(x+1\right)\times 5=\left(x-4\right)\times 5$$

Use the distributive property to multiply x+1 by 5.

$$3x-12+5x+5=\left(x-4\right)\times 5$$

Combine 3x and 5x to get 8x.

$$8x-12+5=\left(x-4\right)\times 5$$

Add -12 and 5 to get -7.

$$8x-7=\left(x-4\right)\times 5$$

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

$$8x-7=5x-20$$

Subtract 5x from both sides.

$$8x-7-5x=-20$$

Combine 8x and -5x to get 3x.

$$3x-7=-20$$

Add 7 to both sides.

$$3x=-20+7$$

Add -20 and 7 to get -13.

$$3x=-13$$

Divide both sides by 3.

$$x=\frac{-13}{3}$$

Fraction \frac{-13}{3} can be rewritten as -\frac{13}{3} by extracting the negative sign.

$$x=-\frac{13}{3}$$