Q33. - Algebra 2

Question

Simplify the expression $\frac{w^2-11w+24}{w^2-18w+80}\cdot \frac{w^2-15w+50}{w^2-9w+20}$

Step-by-Step Solution

Answer

The simplified value of expression is $\frac{w-3}{w-4}$

Step 1. Write down the given expression.

The given expression is $\frac{w^2-11w+24}{w^2-18w+80}\cdot \frac{w^2-15w+50}{w^2-9w+20}$

Step 2. Simplify the expression.

The given expression $\frac{w^2-11w+24}{w^2-18w+80}\cdot \frac{w^2-15w+50}{w^2-9w+20}$is simplified as:

$\begin{array}{c}\frac{w^2-11w+24}{w^2-18w+80}\cdot \frac{w^2-15w+50}{w^2-9w+20}=\frac{\left(w-8\right)\left(w-3\right)}{\left(w-10\right)\left(w-8\right)}\cdot \frac{\left(w-10\right)\left(w-5\right)}{\left(w-4\right)\left(w-5\right)}\\ =\frac{\left(w-3\right)}{\left(w-10\right)}\cdot \frac{\left(w-10\right)}{\left(w-4\right)}\\ =\frac{w-3}{w-4}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{w-3}{w-4}$.