Solve 4v-7/v^2-9v+18+4-3v/v^2-9v+18

$$\frac { 4 v - 7 } { v ^ { 2 } - 9 v + 18 } + \frac { 4 - 3 v } { v ^ { 2 } - 9 v + 18 }$$

Evaluate

$$\frac{1}{v-6}$$

Short Solution Steps

Since \frac{4v-7}{v^{2}-9v+18} and \frac{4-3v}{v^{2}-9v+18} have the same denominator, add them by adding their numerators.

$$\frac{4v-7+4-3v}{v^{2}-9v+18}$$

Combine like terms in 4v-7+4-3v.

$$\frac{v-3}{v^{2}-9v+18}$$

Factor the expressions that are not already factored in \frac{v-3}{v^{2}-9v+18}.

$$\frac{v-3}{\left(v-6\right)\left(v-3\right)}$$

Cancel out v-3 in both numerator and denominator.

$$\frac{1}{v-6}$$

Expand

$$\frac{1}{v-6}$$

Short Solution Steps

Since \frac{4v-7}{v^{2}-9v+18} and \frac{4-3v}{v^{2}-9v+18} have the same denominator, add them by adding their numerators.

$$\frac{4v-7+4-3v}{v^{2}-9v+18}$$

Combine like terms in 4v-7+4-3v.

$$\frac{v-3}{v^{2}-9v+18}$$

Factor the expressions that are not already factored in \frac{v-3}{v^{2}-9v+18}.

$$\frac{v-3}{\left(v-6\right)\left(v-3\right)}$$

Cancel out v-3 in both numerator and denominator.

$$\frac{1}{v-6}$$