The simplified form of the given expression is
.
The steps to simplify a fractional expression are:
- Factorize the expressions both in the numerator and the denominator using different methods
- Remove the common terms in the numerator and denominator
- Thus, the simplified expression will be obtained.
The given expression is
Factorizing the numerator:
x² - 4x - 21 = x² - 7x + 3x - 21
= x(x - 7) + 3(x - 7)
= (x - 7)(x + 3)
Then,
=
common factor (x + 3) is canceled out from both the numerator and the denominator
So,
=
Therefore, the simplified expression is .
Learn more about simplifying an expression here:
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