Solve k+6/9k+10=k+5/9k+5

$$\frac { k + 6 } { 9 k + 10 } = \frac { k + 5 } { 9 k + 5 }$$

Solve for k

$$k=5$$

Steps for Solving Linear Equation

Variable k cannot be equal to any of the values -\frac{10}{9},-\frac{5}{9} since division by zero is not defined. Multiply both sides of the equation by \left(9k+5\right)\left(9k+10\right), the least common multiple of 9k+10,9k+5.

$$\left(9k+5\right)\left(k+6\right)=\left(9k+10\right)\left(k+5\right)$$

Use the distributive property to multiply 9k+5 by k+6 and combine like terms.

$$9k^{2}+59k+30=\left(9k+10\right)\left(k+5\right)$$

Use the distributive property to multiply 9k+10 by k+5 and combine like terms.

$$9k^{2}+59k+30=9k^{2}+55k+50$$

Subtract 9k^{2} from both sides.

$$9k^{2}+59k+30-9k^{2}=55k+50$$

Combine 9k^{2} and -9k^{2} to get 0.

$$59k+30=55k+50$$

Subtract 55k from both sides.

$$59k+30-55k=50$$

Combine 59k and -55k to get 4k.

$$4k+30=50$$

Subtract 30 from both sides.

$$4k=50-30$$

Subtract 30 from 50 to get 20.

$$4k=20$$

Divide both sides by 4.

$$k=\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$k=5$$