Solve 10/x+1=15/4(x+2)

$$\frac { 10 } { x + 1 } = \frac { 15 } { 4 ( x + 2 ) }$$

Solve for x

$$x = -\frac{13}{5} = -2\frac{3}{5} = -2.6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,-1 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+1\right)\left(x+2\right), the least common multiple of x+1,4\left(x+2\right).

$$\left(4x+8\right)\times 10=\left(x+1\right)\times 15$$

Use the distributive property to multiply 4x+8 by 10.

$$40x+80=\left(x+1\right)\times 15$$

Use the distributive property to multiply x+1 by 15.

$$40x+80=15x+15$$

Subtract 15x from both sides.

$$40x+80-15x=15$$

Combine 40x and -15x to get 25x.

$$25x+80=15$$

Subtract 80 from both sides.

$$25x=15-80$$

Subtract 80 from 15 to get -65.

$$25x=-65$$

Divide both sides by 25.

$$x=\frac{-65}{25}$$

Reduce the fraction \frac{-65}{25} to lowest terms by extracting and canceling out 5.

$$x=-\frac{13}{5}$$