Solve (m-3)(m+1)/m-1=1

$$\frac { ( m - 3 ) ( m + 1 ) } { m - 1 } = 1$$

Solve for m

$$m = \frac{\sqrt{17} + 3}{2} \approx 3.561552813$$

$$m=\frac{3-\sqrt{17}}{2}\approx -0.561552813$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by m-1.

$$\left(m-3\right)\left(m+1\right)=m-1$$

Use the distributive property to multiply m-3 by m+1 and combine like terms.

$$m^{2}-2m-3=m-1$$

Subtract m from both sides.

$$m^{2}-2m-3-m=-1$$

Combine -2m and -m to get -3m.

$$m^{2}-3m-3=-1$$

Add 1 to both sides.

$$m^{2}-3m-3+1=0$$

Add -3 and 1 to get -2.

$$m^{2}-3m-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -3 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-2\right)}}{2}$$

Square -3.

$$m=\frac{-\left(-3\right)±\sqrt{9-4\left(-2\right)}}{2}$$

Multiply -4 times -2.

$$m=\frac{-\left(-3\right)±\sqrt{9+8}}{2}$$

Add 9 to 8.

$$m=\frac{-\left(-3\right)±\sqrt{17}}{2}$$

The opposite of -3 is 3.

$$m=\frac{3±\sqrt{17}}{2}$$

Now solve the equation m=\frac{3±\sqrt{17}}{2} when ± is plus. Add 3 to \sqrt{17}.

$$m=\frac{\sqrt{17}+3}{2}$$

Now solve the equation m=\frac{3±\sqrt{17}}{2} when ± is minus. Subtract \sqrt{17} from 3.

$$m=\frac{3-\sqrt{17}}{2}$$

The equation is now solved.

$$m=\frac{\sqrt{17}+3}{2} m=\frac{3-\sqrt{17}}{2}$$

Steps for Completing the Square

Variable m cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by m-1.

$$\left(m-3\right)\left(m+1\right)=m-1$$

Use the distributive property to multiply m-3 by m+1 and combine like terms.

$$m^{2}-2m-3=m-1$$

Subtract m from both sides.

$$m^{2}-2m-3-m=-1$$

Combine -2m and -m to get -3m.

$$m^{2}-3m-3=-1$$

Add 3 to both sides.

$$m^{2}-3m=-1+3$$

Add -1 and 3 to get 2.

$$m^{2}-3m=2$$

Divide -3, the coefficient of the x term, by 2 to get -\frac{3}{2}. Then add the square of -\frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-3m+\left(-\frac{3}{2}\right)^{2}=2+\left(-\frac{3}{2}\right)^{2}$$

Square -\frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-3m+\frac{9}{4}=2+\frac{9}{4}$$

Add 2 to \frac{9}{4}.

$$m^{2}-3m+\frac{9}{4}=\frac{17}{4}$$

Factor m^{2}-3m+\frac{9}{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}.

$$\left(m-\frac{3}{2}\right)^{2}=\frac{17}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{3}{2}\right)^{2}}=\sqrt{\frac{17}{4}}$$

Simplify.

$$m-\frac{3}{2}=\frac{\sqrt{17}}{2} m-\frac{3}{2}=-\frac{\sqrt{17}}{2}$$

Add \frac{3}{2} to both sides of the equation.

$$m=\frac{\sqrt{17}+3}{2} m=\frac{3-\sqrt{17}}{2}$$