Simplify: x² - 5x - 14/x² - 9x + 14

Correct Answer is : x+2x−2x + 2/x - 2x−2x+2

Correct Answer is : x+2x−2x + 2/x - 2x−2x+2

Test Index

WAEC Mathematics 2019 Paper

Question : 19

Total: 50

Simplify:

\frac{x^2 - 5x - 14}{x^2 - 9x + 14}

Solution:

Concept:

Factorising quadratic expressions to simplify a rational algebraic fraction by cancelling common factors.

Explanation:

Factorise the numerator:

x^2 - 5x - 14 = (x - 7)(x + 2)

Factorise the denominator:

x^2 - 9x + 14 = (x - 7)(x - 2)

Substitute the factors into the fraction:

\frac{x^2 - 5x - 14}{x^2 - 9x + 14} = \frac{(x - 7)(x + 2)}{(x - 7)(x - 2)}

Cancel the common factor

(x - 7)

from the numerator and denominator:

= \frac{x + 2}{x - 2}

This simplification is valid for

x \neq 7

Answer:

\frac{x + 2}{x - 2}

Option D.

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