The quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]
How to determine the quotient?
The expression is given as:
[tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]
Express x^2 - 49 as difference of two squares
[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]
Factorize other expressions
[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{(x -7)(x-7)}{3(x + 2)}[/tex]
Express as product
[tex]\frac{(x + 7)(x- 7)}{x + 2} \times\frac{3(x + 2)}{(x -7)(x-7)}[/tex]
Cancel the common factors
[tex]\frac{(x + 7)}{1} \times\frac{3}{(x -7)}[/tex]
Evaluate the product
[tex]\frac{3(x +7)}{(x -7)}[/tex]
Hence, the quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]
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