Question

What is the simplified form of the expression the quantity x squared minus 4x minus 21 end quantity divided by 4 times the quantity x plus 3 end quantity?

Answer 1

The simplified form of the given expression $\frac{x^2-4x-21}{4(x+3)}$ is $\frac{x-7}{4}$.

How to simplify a fractional expression?

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.

Calculation:

The given expression is $\frac{x^2-4x-21}{4(x+3)}$

Factorizing the numerator:

x² - 4x - 21 = x² - 7x + 3x - 21

                 = x(x - 7) + 3(x - 7)

                 = (x - 7)(x + 3)

Then,

$\frac{x^2-4x-21}{4(x+3)}$ = $\frac{(x-7)(x+3)}{4(x+3)}$

common factor (x + 3) is canceled out from both the numerator and the denominator

So,

$\frac{x^2-4x-21}{4(x+3)}$ = $\frac{x-7}{4}$

Therefore, the simplified expression is $\frac{x-7}{4}$.

Learn more about simplifying an expression here:

brainly.com/question/13742517

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