Solve 5/x^2+2x-3+45/x^2+10x+21=18/x^2+6x-7

$$\frac { 5 } { x ^ { 2 } + 2 x - 3 } + \frac { 45 } { x ^ { 2 } + 10 x + 21 } = \frac { 18 } { x ^ { 2 } + 6 x - 7 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -7,-3,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+3\right)\left(x+7\right), the least common multiple of x^{2}+2x-3,x^{2}+10x+21,x^{2}+6x-7.

$$\left(x+7\right)\times 5+\left(x-1\right)\times 45=\left(x+3\right)\times 18$$

Use the distributive property to multiply x+7 by 5.

$$5x+35+\left(x-1\right)\times 45=\left(x+3\right)\times 18$$

Use the distributive property to multiply x-1 by 45.

$$5x+35+45x-45=\left(x+3\right)\times 18$$

Combine 5x and 45x to get 50x.

$$50x+35-45=\left(x+3\right)\times 18$$

Subtract 45 from 35 to get -10.

$$50x-10=\left(x+3\right)\times 18$$

Use the distributive property to multiply x+3 by 18.

$$50x-10=18x+54$$

Subtract 18x from both sides.

$$50x-10-18x=54$$

Combine 50x and -18x to get 32x.

$$32x-10=54$$

Add 10 to both sides.

$$32x=54+10$$

Add 54 and 10 to get 64.

$$32x=64$$

Divide both sides by 32.

$$x=\frac{64}{32}$$

Divide 64 by 32 to get 2.

$$x=2$$