Solve 2/2x^2+7x+3-1/2x^2+11x+5=1/x^2+8x+15

$$\frac{ 2 }{ 2 { x }^{ 2 } +7x+3 } - \frac{ 1 }{ 2 { x }^{ 2 } +11x+5 } = \frac{ 1 }{ { x }^{ 2 } +8x+15 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,-3,-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)\left(x+5\right)\left(2x+1\right), the least common multiple of 2x^{2}+7x+3,2x^{2}+11x+5,x^{2}+8x+15.

$$\left(x+5\right)\times 2-\left(x+3\right)=2x+1$$

Use the distributive property to multiply x+5 by 2.

$$2x+10-\left(x+3\right)=2x+1$$

To find the opposite of x+3, find the opposite of each term.

$$2x+10-x-3=2x+1$$

Combine 2x and -x to get x.

$$x+10-3=2x+1$$

Subtract 3 from 10 to get 7.

$$x+7=2x+1$$

Subtract 2x from both sides.

$$x+7-2x=1$$

Combine x and -2x to get -x.

$$-x+7=1$$

Subtract 7 from both sides.

$$-x=1-7$$

Subtract 7 from 1 to get -6.

$$-x=-6$$

Multiply both sides by -1.

$$x=6$$