Solve x-2/x+3=2x^2+x-10/x^2+6x+9

$$\frac { x - 2 } { x + 3 } = \frac { 2 x ^ { 2 } + x - 10 } { x ^ { 2 } + 6 x + 9 }$$

Solve for x

$$x=-2$$

$$x=2$$

Steps by Finding Square Root

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)^{2}, the least common multiple of x+3,x^{2}+6x+9.

$$\left(x+3\right)\left(x-2\right)=2x^{2}+x-10$$

Use the distributive property to multiply x+3 by x-2 and combine like terms.

$$x^{2}+x-6=2x^{2}+x-10$$

Subtract 2x^{2} from both sides.

$$x^{2}+x-6-2x^{2}=x-10$$

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

$$-x^{2}+x-6=x-10$$

Subtract x from both sides.

$$-x^{2}+x-6-x=-10$$

Combine x and -x to get 0.

$$-x^{2}-6=-10$$

Add 6 to both sides.

$$-x^{2}=-10+6$$

Add -10 and 6 to get -4.

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

Divide both sides by -1.

$$x^{2}=\frac{-4}{-1}$$

Fraction \frac{-4}{-1} can be simplified to 4 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)^{2}, the least common multiple of x+3,x^{2}+6x+9.

$$\left(x+3\right)\left(x-2\right)=2x^{2}+x-10$$

Use the distributive property to multiply x+3 by x-2 and combine like terms.

$$x^{2}+x-6=2x^{2}+x-10$$

Subtract 2x^{2} from both sides.

$$x^{2}+x-6-2x^{2}=x-10$$

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

$$-x^{2}+x-6=x-10$$

Subtract x from both sides.

$$-x^{2}+x-6-x=-10$$

Combine x and -x to get 0.

$$-x^{2}-6=-10$$

Add 10 to both sides.

$$-x^{2}-6+10=0$$

Add -6 and 10 to get 4.

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

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 4}}{2\left(-1\right)}$$

Multiply 4 times 4.

$$x=\frac{0±\sqrt{16}}{2\left(-1\right)}$$

Take the square root of 16.

$$x=\frac{0±4}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4}{-2}$$

Now solve the equation x=\frac{0±4}{-2} when ± is plus. Divide 4 by -2.

$$x=-2$$

Now solve the equation x=\frac{0±4}{-2} when ± is minus. Divide -4 by -2.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$