Solve x/x+2+8/7-1/5=4

$$\frac { x } { x + 2 } + \frac { 8 } { 7 } - \frac { 1 } { 5 } = 4$$

Solve for x

$$x = -\frac{107}{36} = -2\frac{35}{36} \approx -2.972222222$$

Steps for Solving Linear Equation

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 35\left(x+2\right), the least common multiple of x+2,7,5.

$$35x+35\left(x+2\right)\times \frac{8}{7}+35\left(x+2\right)\left(-\frac{1}{5}\right)=140\left(x+2\right)$$

Multiply 35 and \frac{8}{7} to get 40.

$$35x+40\left(x+2\right)+35\left(x+2\right)\left(-\frac{1}{5}\right)=140\left(x+2\right)$$

Use the distributive property to multiply 40 by x+2.

$$35x+40x+80+35\left(x+2\right)\left(-\frac{1}{5}\right)=140\left(x+2\right)$$

Combine 35x and 40x to get 75x.

$$75x+80+35\left(x+2\right)\left(-\frac{1}{5}\right)=140\left(x+2\right)$$

Multiply 35 and -\frac{1}{5} to get -7.

$$75x+80-7\left(x+2\right)=140\left(x+2\right)$$

Use the distributive property to multiply -7 by x+2.

$$75x+80-7x-14=140\left(x+2\right)$$

Combine 75x and -7x to get 68x.

$$68x+80-14=140\left(x+2\right)$$

Subtract 14 from 80 to get 66.

$$68x+66=140\left(x+2\right)$$

Use the distributive property to multiply 140 by x+2.

$$68x+66=140x+280$$

Subtract 140x from both sides.

$$68x+66-140x=280$$

Combine 68x and -140x to get -72x.

$$-72x+66=280$$

Subtract 66 from both sides.

$$-72x=280-66$$

Subtract 66 from 280 to get 214.

$$-72x=214$$

Divide both sides by -72.

$$x=\frac{214}{-72}$$

Reduce the fraction \frac{214}{-72} to lowest terms by extracting and canceling out 2.

$$x=-\frac{107}{36}$$