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How do you simplify #(5x^2+10x)/(x^2-x-6)div(15x^3+45x^2)/(x^2-9)#?

Answer 1

Eva Abramson

#1/(3x)#

To simplify, it is advisable to factorise the expressions first and then see if some get cancelled out.

=#(5x(x+2))/((x-3)(x+2)) div (15x^2(x+3))/((x-3)(x+3))#

=#(5x)/(x-3) div (15x^2)/(x-3) #

=# (5x)/(x-3) * (x-3)/(15x^2)#

= #1/(3x)#

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Answer 2

Jace Anderson

To simplify the expression (5x^2+10x)/(x^2-x-6) ÷ (15x^3+45x^2)/(x^2-9), we can follow these steps:

Factorize the denominators: (x^2-x-6) = (x-3)(x+2) (x^2-9) = (x-3)(x+3)
Rewrite the expression using the factored denominators: (5x^2+10x)/[(x-3)(x+2)] ÷ (15x^3+45x^2)/[(x-3)(x+3)]
Invert the second fraction and change the division to multiplication: (5x^2+10x)/[(x-3)(x+2)] * [(x-3)(x+3)]/(15x^3+45x^2)
Cancel out common factors between the numerators and denominators: (5x^2+10x)/(15x^2) * (x+3)/(x+2)
Simplify the expression further: (x+2)(x+3)/(3x^2)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.