Question

simplify x²-49/3x+21

Answer 1

First, you factor and simplify (respectively) the numerator and denominator. Your equation becomes:

$\frac{(x-7)(x+7)}{3(x + 7)}$

Notice, there is a (x + 7) on both the top and the bottom. Because of this, they cancel each other out. What is left is your answer:

$\frac{(x-7)}{3}$

Answer 2

The simplified expression of $\mathbf{\frac{x^2 - 49}{3x + 21} }$ is $\mathbf{\frac{x - 7}{3}}$

The expression is given as:

$\mathbf{\frac{x^2 - 49}{3x + 21}}$

Express 49 as 7^2

$\mathbf{\frac{x^2 - 49}{3x + 21} = \frac{x^2 - 7^2}{3x + 21}}$

Express x^2 - 7^2 as difference of two squares

$\mathbf{\frac{x^2 - 49}{3x + 21} = \frac{(x - 7)(x + 7)}{3x + 21}}$

Factor out 3

$\mathbf{\frac{x^2 - 49}{3x + 21} = \frac{(x - 7)(x + 7)}{3(x + 7)}}$

Cancel out common factor: x + 7

$\mathbf{\frac{x^2 - 49}{3x + 21} = \frac{x - 7}{3}}$

Hence, the simplified expression of $\mathbf{\frac{x^2 - 49}{3x + 21} }$ is $\mathbf{\frac{x - 7}{3}}$

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