Question

Find each sum or difference.

$\frac{t-5}{t-6}+\frac{t+8}{t-6}$

Short answer

$\frac{\mathbf{2}\mathbf{t}\mathbf{+}\mathbf{3}}{\mathbf{t}\mathbf{-}\mathbf{6}}$

Step-by-step solution

Step 1. Add.

Let $x,y$ and $z$ be polynomials with $z\ne 0$, such that, $\frac{x}{z}+\frac{y}{z}=\frac{x+y}{z}$.

Step 2. Add.

Find the sum.

$\frac{t-5}{t-6}+\frac{t+8}{t-6}=\frac{\left(t-5\right)+\left(t+8\right)}{t-6}$

Step 3. Simplify.

Simplify the obtained expression.

$\frac{t+t-5+8}{t-6}=\frac{2t+3}{t-6}$

Therefore, the sum of the given expression is $\frac{2t+3}{t-6}$.