I need help with simplifying this expression?

[chaishreen]

(x^2 - 9) / (15 - 5x)

Also, I need to state any restrictions on the variable

the answer at the back of the textbook says:
- x - 3/5, x is not equal to 3

 

[Deleted member 4993]

(x^2 - 9) / (15 - 5x)

Also, I need to state any restrictions on the variable

the answer at the back of the textbook says:
- x - 3/5, x is not equal to 3

x² - 9 = x² - 3²

Factorize the numerator and the denominator of the given expression.

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[stapel]

I need help with simplifying this expression?

(x^2 - 9) / (15 - 5x)

Also, I need to state any restrictions on the variable

As the first reply suggested, factorization will be a helpful way to begin. The reply provided you with the set-up for factorizing the numerator, which involves factoring a difference of squares. (link) To factorize the denominator, you'll need to apply the simple factorization techniques you have learned. (link)

The simplification is, as is always the case with fractions, a matter of cancellation. (link) The domain of the simplified expression must be restricted in order to cause it to match the domain of the original expression, being the expression before the cancellation got rid of a restriction on the domain. In graphing, this is called "the case with the hole". (link)