MHB Algebraic Rational Expressions

AI Thread Summary
The discussion focuses on simplifying the algebraic expression $$\frac{5a^5b^6}{10a^2b^3}\div\frac{2a^4b^2}{20a^3b^5}$$ and identifying restrictions on the variables. Participants clarify that the denominators must not equal zero, which means both variables a and b cannot be zero. The process of simplification involves canceling common factors in the numerator and denominator after inverting the second fraction. The main takeaway is that understanding the restrictions is crucial for defining the expression and performing the simplification correctly. Overall, the discussion emphasizes the importance of identifying variable restrictions in algebraic rational expressions.
jjlittle00
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I am attempting to find the solution to the following question.

Simplify and state the restrictions on the variables$$\frac{5a^5b^6}{10a^2b^3}\div\frac{2a^4b^2}{20a^3b^5}$$

Not really understanding how to find the restrictions with these set variables.
 
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Hello and welcome to MHB, jjlittle00! (Wave)

I am assuming the expression is as follows:

$$\frac{5a^5b^6}{10a^2b^3}\div\frac{2a^2b^3}{20a^2b^3}$$

Before we proceed, is this correct?
 
MarkFL said:
Hello and welcome to MHB, jjlittle00! (Wave)

I am assuming the expression is as follows:

$$\frac{5a^5b^6}{10a^2b^3}\div\frac{2a^4b^2}{20a^3b^5}$$

Before we proceed, is this correct?
Yes this is correct. Just made one small correction.
 
jjlittle00 said:
Yes this is correct. Just made one small correction.

Okay, we now have:

$$\frac{5a^5b^6}{10a^2b^3}\div\frac{2a^4b^2}{20a^3b^5}$$

We have one rational expression being divided by another. In order for these expressions to be defined, we cannot have either denominator being equal to zero. What values of $a$ and/or $b$ will cause either denominator to be zero?
 
Also, when we divide by a fraction, we "invert and multiply": \frac{5a^5b^6}{10a^2b^3}\frac{20a^3b^5}{2a^4b^2}. So that, in addition to the requirement that the denominators of the original fractions not being 0, 2a^4b^2 cannot be 0. That is effectively saying that a and b cannot be 0.

Of course, to "simplify" you cancel as many "a"s and "b"s, in numerator and denominator, as you can.
 
HallsofIvy said:
Also, when we divide by a fraction, we "invert and multiply": \frac{5a^5b^6}{10a^2b^3}\frac{20a^3b^5}{2a^4b^2}. So that, in addition to the requirement that the denominators of the original fractions not being 0, 2a^4b^2 cannot be 0. That is effectively saying that a and b cannot be 0.

Of course, to "simplify" you cancel as many "a"s and "b"s, in numerator and denominator, as you can.

I was going to get to all that eventually...honest I was...:p
 
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