Solve m+3/m-2=m+5/m-5

$$\frac { m + 3 } { m - 2 } = \frac { m + 5 } { m - 5 }$$

Solve for m

$$m=-1$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply m-5 by m+3 and combine like terms.

$$m^{2}-2m-15=\left(m-2\right)\left(m+5\right)$$

Use the distributive property to multiply m-2 by m+5 and combine like terms.

$$m^{2}-2m-15=m^{2}+3m-10$$

Subtract m^{2} from both sides.

$$m^{2}-2m-15-m^{2}=3m-10$$

Combine m^{2} and -m^{2} to get 0.

$$-2m-15=3m-10$$

Subtract 3m from both sides.

$$-2m-15-3m=-10$$

Combine -2m and -3m to get -5m.

$$-5m-15=-10$$

Add 15 to both sides.

$$-5m=-10+15$$

Add -10 and 15 to get 5.

$$-5m=5$$

Divide both sides by -5.

$$m=\frac{5}{-5}$$

Divide 5 by -5 to get -1.

$$m=-1$$