Home > Algebra > Excluded Values for Rational Expressions

How do you simplify #(45a^5b(8-a))/(20a^2b^3(a-8))# and what are the restrictions?

Answer 1

Genesis Allen

Given #(45a^5b(8-a))/(20a^2b^3(a-8)#

This expression is only defined if the denominator is not equal to zero; therefore #a!=0, b!=0, a!=8#

#(45a^5b(8-a))/(20a^2b^3(a-8)#

#= color(red)(45/20) * color(green)((a^5)/(a^2)) * color(orange)((b)/(b^3)) * color(blue)((8-a)/(a-8))#

#= color(red)(9/4) * color(green)(a^3) * color(orange)(1/(b^2)) * color(blue)((-1))#

#= - (9a^3)/(4b^2)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Savannah Anderson

To simplify the expression (45a^5b(8-a))/(20a^2b^3(a-8)), we can cancel out common factors in the numerator and denominator.

First, cancel out the common factors of 5, a, and b: (45a^5b(8-a))/(20a^2b^3(a-8)) = (9a^4(8-a))/(4b^2(a-8))

Next, simplify further by expanding the numerator: (9a^4(8-a))/(4b^2(a-8)) = (72a^4 - 9a^5)/(4b^2(a-8))

The restrictions for this expression are that a cannot equal 0, a cannot equal 8, and b cannot equal 0.

By signing up, you agree to our Terms of Service and Privacy Policy

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.