Question

question 6
2 pts
simplify each expression.
\\(\frac{4x - 20}{x + 10} \div \frac{x^2 - 8x + 15}{x + 10}\\)
numerator / denominator =

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{4x - 20}{x + 10}\div\frac{x^{2}-8x + 15}{x + 10}=\frac{4x - 20}{x + 10}\times\frac{x + 10}{x^{2}-8x + 15}\)

Step2: Factor numerators and denominators

• Factor \(4x - 20\): We can factor out a 4, so \(4x - 20 = 4(x - 5)\)
• Factor \(x^{2}-8x + 15\): We need two numbers that multiply to 15 and add to -8. Those numbers are -3 and -5. So, \(x^{2}-8x + 15=(x - 3)(x - 5)\)

Substituting these factorizations into the expression, we get:
\(\frac{4(x - 5)}{x + 10}\times\frac{x + 10}{(x - 3)(x - 5)}\)

Step3: Cancel common factors

We can cancel out the common factors \((x - 5)\) and \((x + 10)\) from the numerator and the denominator.
After canceling, we are left with \(\frac{4}{x - 3}\)

Answer:

\(4\) / \(x - 3\)