Solve w+7/w+6=w+5/w+3

$$\frac { w + 7 } { w + 6 } = \frac { w + 5 } { w + 3 }$$

Solve for w

$$w=-9$$

Steps for Solving Linear Equation

Variable w cannot be equal to any of the values -6,-3 since division by zero is not defined. Multiply both sides of the equation by \left(w+3\right)\left(w+6\right), the least common multiple of w+6,w+3.

$$\left(w+3\right)\left(w+7\right)=\left(w+6\right)\left(w+5\right)$$

Use the distributive property to multiply w+3 by w+7 and combine like terms.

$$w^{2}+10w+21=\left(w+6\right)\left(w+5\right)$$

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

$$w^{2}+10w+21=w^{2}+11w+30$$

Subtract w^{2} from both sides.

$$w^{2}+10w+21-w^{2}=11w+30$$

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

$$10w+21=11w+30$$

Subtract 11w from both sides.

$$10w+21-11w=30$$

Combine 10w and -11w to get -w.

$$-w+21=30$$

Subtract 21 from both sides.

$$-w=30-21$$

Subtract 21 from 30 to get 9.

$$-w=9$$

Multiply both sides by -1.

$$w=-9$$