Solve 2-5/x+2=13/5

$$2 - \frac { 5 } { x + 2 } = 1 \frac { 3 } { 5 }$$

Solve for x

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

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 5\left(x+2\right), the least common multiple of x+2,5.

$$5\left(x+2\right)\times 2-5\times 5=\left(x+2\right)\left(1\times 5+3\right)$$

Use the distributive property to multiply 5 by x+2.

$$\left(5x+10\right)\times 2-5\times 5=\left(x+2\right)\left(1\times 5+3\right)$$

Use the distributive property to multiply 5x+10 by 2.

$$10x+20-5\times 5=\left(x+2\right)\left(1\times 5+3\right)$$

Multiply -5 and 5 to get -25.

$$10x+20-25=\left(x+2\right)\left(1\times 5+3\right)$$

Subtract 25 from 20 to get -5.

$$10x-5=\left(x+2\right)\left(1\times 5+3\right)$$

Multiply 1 and 5 to get 5.

$$10x-5=\left(x+2\right)\left(5+3\right)$$

Add 5 and 3 to get 8.

$$10x-5=\left(x+2\right)\times 8$$

Use the distributive property to multiply x+2 by 8.

$$10x-5=8x+16$$

Subtract 8x from both sides.

$$10x-5-8x=16$$

Combine 10x and -8x to get 2x.

$$2x-5=16$$

Add 5 to both sides.

$$2x=16+5$$

Add 16 and 5 to get 21.

$$2x=21$$

Divide both sides by 2.

$$x=\frac{21}{2}$$