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How do you simplify and find the excluded values for #(2a^2+10a)/(3a^2+15a)#?

Answer 1

Expression simplifies to #2/3 and a!=0 and a!=-5#

Factorize top and bottom by taking out a common factor to obtain

#(2a(a+5))/(3a(a+5)#

We now cancel to yield #2/3#

Now the excluded values, also called the restrictions, are values that would make the denominator equal to zero as this would be undefined. These values would be #a=0 and a=-5#

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Answer 2

Nathan Axel

To simplify the expression (2a^2+10a)/(3a^2+15a), we can factor out a common factor of 2a from both the numerator and denominator. This gives us (2a(a+5))/(3a(a+5)).

Next, we can cancel out the common factor of (a+5) from both the numerator and denominator. This leaves us with 2a/3a, which simplifies to 2/3.

To find the excluded values, we need to identify the values of 'a' that would make the denominator equal to zero. In this case, if we set 3a^2+15a equal to zero and solve for 'a', we get a = 0 and a = -5. Therefore, the excluded values are a = 0 and a = -5.

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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.