Solve 20x/5x+1+6/x+6=4

$$\frac { 20 x } { 5 x + 1 } + \frac { 6 } { x + 6 } = 4$$

Solve for x

$$x=\frac{9}{13}\approx 0.692307692$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,-\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by \left(x+6\right)\left(5x+1\right), the least common multiple of 5x+1,x+6.

$$\left(x+6\right)\times 20x+\left(5x+1\right)\times 6=4\left(x+6\right)\left(5x+1\right)$$

Use the distributive property to multiply x+6 by 20.

$$\left(20x+120\right)x+\left(5x+1\right)\times 6=4\left(x+6\right)\left(5x+1\right)$$

Use the distributive property to multiply 20x+120 by x.

$$20x^{2}+120x+\left(5x+1\right)\times 6=4\left(x+6\right)\left(5x+1\right)$$

Use the distributive property to multiply 5x+1 by 6.

$$20x^{2}+120x+30x+6=4\left(x+6\right)\left(5x+1\right)$$

Combine 120x and 30x to get 150x.

$$20x^{2}+150x+6=4\left(x+6\right)\left(5x+1\right)$$

Use the distributive property to multiply 4 by x+6.

$$20x^{2}+150x+6=\left(4x+24\right)\left(5x+1\right)$$

Use the distributive property to multiply 4x+24 by 5x+1 and combine like terms.

$$20x^{2}+150x+6=20x^{2}+124x+24$$

Subtract 20x^{2} from both sides.

$$20x^{2}+150x+6-20x^{2}=124x+24$$

Combine 20x^{2} and -20x^{2} to get 0.

$$150x+6=124x+24$$

Subtract 124x from both sides.

$$150x+6-124x=24$$

Combine 150x and -124x to get 26x.

$$26x+6=24$$

Subtract 6 from both sides.

$$26x=24-6$$

Subtract 6 from 24 to get 18.

$$26x=18$$

Divide both sides by 26.

$$x=\frac{18}{26}$$

Reduce the fraction \frac{18}{26} to lowest terms by extracting and canceling out 2.

$$x=\frac{9}{13}$$