Solve x-5/x^2+3x+2=2/4x+4-3/x+2

$$\frac { x - 5 } { x ^ { 2 } + 3 x + 2 } = \frac { 2 } { 4 x + 4 } - \frac { 3 } { x + 2 }$$

Solve for x

$$x=\frac{6}{7}\approx 0.857142857$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,-1 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+1\right)\left(x+2\right), the least common multiple of x^{2}+3x+2,4x+4,x+2.

$$4\left(x-5\right)=\left(x+2\right)\times 2-\left(4x+4\right)\times 3$$

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

$$4x-20=\left(x+2\right)\times 2-\left(4x+4\right)\times 3$$

Use the distributive property to multiply x+2 by 2.

$$4x-20=2x+4-\left(4x+4\right)\times 3$$

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

$$4x-20=2x+4-\left(12x+12\right)$$

To find the opposite of 12x+12, find the opposite of each term.

$$4x-20=2x+4-12x-12$$

Combine 2x and -12x to get -10x.

$$4x-20=-10x+4-12$$

Subtract 12 from 4 to get -8.

$$4x-20=-10x-8$$

Add 10x to both sides.

$$4x-20+10x=-8$$

Combine 4x and 10x to get 14x.

$$14x-20=-8$$

Add 20 to both sides.

$$14x=-8+20$$

Add -8 and 20 to get 12.

$$14x=12$$

Divide both sides by 14.

$$x=\frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{6}{7}$$