Solve m+3/3=8/m-2

$$\frac { m + 3 } { 3 } = \frac { 8 } { m - 2 }$$

Solve for m

$$m=-6$$

$$m=5$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 3\left(m-2\right), the least common multiple of 3,m-2.

$$\left(m-2\right)\left(m+3\right)=3\times 8$$

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

$$m^{2}+m-6=3\times 8$$

Multiply 3 and 8 to get 24.

$$m^{2}+m-6=24$$

Subtract 24 from both sides.

$$m^{2}+m-6-24=0$$

Subtract 24 from -6 to get -30.

$$m^{2}+m-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-1±\sqrt{1^{2}-4\left(-30\right)}}{2}$$

Square 1.

$$m=\frac{-1±\sqrt{1-4\left(-30\right)}}{2}$$

Multiply -4 times -30.

$$m=\frac{-1±\sqrt{1+120}}{2}$$

Add 1 to 120.

$$m=\frac{-1±\sqrt{121}}{2}$$

Take the square root of 121.

$$m=\frac{-1±11}{2}$$

Now solve the equation m=\frac{-1±11}{2} when ± is plus. Add -1 to 11.

$$m=\frac{10}{2}$$

Divide 10 by 2.

$$m=5$$

Now solve the equation m=\frac{-1±11}{2} when ± is minus. Subtract 11 from -1.

$$m=-\frac{12}{2}$$

Divide -12 by 2.

$$m=-6$$

The equation is now solved.

$$m=5 m=-6$$

Steps for Completing the Square

Variable m cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 3\left(m-2\right), the least common multiple of 3,m-2.

$$\left(m-2\right)\left(m+3\right)=3\times 8$$

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

$$m^{2}+m-6=3\times 8$$

Multiply 3 and 8 to get 24.

$$m^{2}+m-6=24$$

Add 6 to both sides.

$$m^{2}+m=24+6$$

Add 24 and 6 to get 30.

$$m^{2}+m=30$$

Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}+m+\left(\frac{1}{2}\right)^{2}=30+\left(\frac{1}{2}\right)^{2}$$

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$m^{2}+m+\frac{1}{4}=30+\frac{1}{4}$$

Add 30 to \frac{1}{4}.

$$m^{2}+m+\frac{1}{4}=\frac{121}{4}$$

Factor m^{2}+m+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m+\frac{1}{2}\right)^{2}=\frac{121}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m+\frac{1}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Simplify.

$$m+\frac{1}{2}=\frac{11}{2} m+\frac{1}{2}=-\frac{11}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$m=5 m=-6$$