Solve x+2/x+5=4/x+2

$$\frac { x + 2 } { x + 5 } = \frac { 4 } { x + 2 }$$

Solve for x

$$x=-4$$

$$x=4$$

Steps by Finding Square Root

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

$$\left(x+2\right)\left(x+2\right)=\left(x+5\right)\times 4$$

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

Use the distributive property to multiply x+5 by 4.

$$x^{2}+4x+4=4x+20$$

Subtract 4x from both sides.

$$x^{2}+4x+4-4x=20$$

Combine 4x and -4x to get 0.

$$x^{2}+4=20$$

Subtract 4 from both sides.

$$x^{2}=20-4$$

Subtract 4 from 20 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

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

$$\left(x+2\right)\left(x+2\right)=\left(x+5\right)\times 4$$

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

Use the distributive property to multiply x+5 by 4.

$$x^{2}+4x+4=4x+20$$

Subtract 4x from both sides.

$$x^{2}+4x+4-4x=20$$

Combine 4x and -4x to get 0.

$$x^{2}+4=20$$

Subtract 20 from both sides.

$$x^{2}+4-20=0$$

Subtract 20 from 4 to get -16.

$$x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$x=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$x=\frac{0±8}{2}$$

Now solve the equation x=\frac{0±8}{2} when ± is plus. Divide 8 by 2.

$$x=4$$

Now solve the equation x=\frac{0±8}{2} when ± is minus. Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$