Solve 2w^2+1/w^2-7w+6-w^2-7w+9/w^2-7w+6

$$\frac { 2 w ^ { 2 } + 1 } { w ^ { 2 } - 7 w + 6 } - \frac { w ^ { 2 } - 7 w + 9 } { w ^ { 2 } - 7 w + 6 }$$

Evaluate

$$\frac{w+8}{w-6}$$

Short Solution Steps

Since \frac{2w^{2}+1}{w^{2}-7w+6} and \frac{w^{2}-7w+9}{w^{2}-7w+6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2w^{2}+1-\left(w^{2}-7w+9\right)}{w^{2}-7w+6}$$

Do the multiplications in 2w^{2}+1-\left(w^{2}-7w+9\right).

$$\frac{2w^{2}+1-w^{2}+7w-9}{w^{2}-7w+6}$$

Combine like terms in 2w^{2}+1-w^{2}+7w-9.

$$\frac{w^{2}-8+7w}{w^{2}-7w+6}$$

Factor the expressions that are not already factored in \frac{w^{2}-8+7w}{w^{2}-7w+6}.

$$\frac{\left(w-1\right)\left(w+8\right)}{\left(w-6\right)\left(w-1\right)}$$

Cancel out w-1 in both numerator and denominator.

$$\frac{w+8}{w-6}$$

Expand

$$\frac{w+8}{w-6}$$

Short Solution Steps

Since \frac{2w^{2}+1}{w^{2}-7w+6} and \frac{w^{2}-7w+9}{w^{2}-7w+6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2w^{2}+1-\left(w^{2}-7w+9\right)}{w^{2}-7w+6}$$

Do the multiplications in 2w^{2}+1-\left(w^{2}-7w+9\right).

$$\frac{2w^{2}+1-w^{2}+7w-9}{w^{2}-7w+6}$$

Combine like terms in 2w^{2}+1-w^{2}+7w-9.

$$\frac{w^{2}-8+7w}{w^{2}-7w+6}$$

Factor the expressions that are not already factored in \frac{w^{2}-8+7w}{w^{2}-7w+6}.

$$\frac{\left(w-1\right)\left(w+8\right)}{\left(w-6\right)\left(w-1\right)}$$

Cancel out w-1 in both numerator and denominator.

$$\frac{w+8}{w-6}$$