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How do you simplify the expression #(4a^2b+8ab)/(6a^2-6a)#?

Answer 1

Savannah Anderson

See a solution process below:

First, rewrite the numerator and denominator by factoring out common terms:

#((4ab * a) + (4ab * 2))/((6a * a) - (6a * 1)) => (4ab(a + 2))/(6a(a - 1))#

Now, cancel common terms in the numerator and denominator:

#(4ab(a + 2))/(6a(a - 1)) => ((2 xx 2)ab(a + 2))/((2 xx 3)a(a - 1)) => #

#((color(red)(cancel(color(black)(2))) xx 2)color(blue)(cancel(color(black)(a)))b(a + 2))/((color(red)(cancel(color(black)(2))) xx 3)color(blue)(cancel(color(black)(a)))(a - 1)) => (2b(a + 2))/(3(a - 1))#

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Answer 2

Julia Adams

To simplify the expression (4a^2b+8ab)/(6a^2-6a), you can factor out the greatest common factor from both the numerator and the denominator. In this case, the greatest common factor is 2ab. Factoring it out, we get:

(2ab(2a+4))/(6a(a-1))

Next, we can simplify further by canceling out common factors. In this case, we can cancel out the 2a from the numerator and the denominator:

(2b(2a+4))/(3(a-1))

Therefore, the simplified expression is (2b(2a+4))/(3(a-1)).

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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.