Solve 4x-1/x+7+4x+7/x-3=8

$$\frac { 4 x - 1 } { x + 7 } + \frac { 4 x + 7 } { x - 3 } = 8$$

Solve for x

$$x=22$$

Steps for Solving Linear Equation

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

$$\left(x-3\right)\left(4x-1\right)+\left(x+7\right)\left(4x+7\right)=8\left(x-3\right)\left(x+7\right)$$

Use the distributive property to multiply x-3 by 4x-1 and combine like terms.

$$4x^{2}-13x+3+\left(x+7\right)\left(4x+7\right)=8\left(x-3\right)\left(x+7\right)$$

Use the distributive property to multiply x+7 by 4x+7 and combine like terms.

$$4x^{2}-13x+3+4x^{2}+35x+49=8\left(x-3\right)\left(x+7\right)$$

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$8x^{2}-13x+3+35x+49=8\left(x-3\right)\left(x+7\right)$$

Combine -13x and 35x to get 22x.

$$8x^{2}+22x+3+49=8\left(x-3\right)\left(x+7\right)$$

Add 3 and 49 to get 52.

$$8x^{2}+22x+52=8\left(x-3\right)\left(x+7\right)$$

Use the distributive property to multiply 8 by x-3.

$$8x^{2}+22x+52=\left(8x-24\right)\left(x+7\right)$$

Use the distributive property to multiply 8x-24 by x+7 and combine like terms.

$$8x^{2}+22x+52=8x^{2}+32x-168$$

Subtract 8x^{2} from both sides.

$$8x^{2}+22x+52-8x^{2}=32x-168$$

Combine 8x^{2} and -8x^{2} to get 0.

$$22x+52=32x-168$$

Subtract 32x from both sides.

$$22x+52-32x=-168$$

Combine 22x and -32x to get -10x.

$$-10x+52=-168$$

Subtract 52 from both sides.

$$-10x=-168-52$$

Subtract 52 from -168 to get -220.

$$-10x=-220$$

Divide both sides by -10.

$$x=\frac{-220}{-10}$$

Divide -220 by -10 to get 22.

$$x=22$$