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I am trying to solve a worksheet that has questions related to Rational Expressions and one of the questions in that worksheet asks us to simplify and find the excluded value of a rational expression. I got to solve a question that was:- Rational Expression

As I Simplified I the above rational Expression I got:- Simplified Expression

Now I know that if want to find the excluded value than I need to make the denominator equal to zero and I would get the excluded value that is {0, -5} without simplifying but I would like to know that if I do simplify than is there any way that I can get the excluded value from the simplified expression.

Thanks

Sohaib Farooq
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1 Answers1

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Hint: You can factor out $\frac23$ in the numerator.

$$\frac{\frac23\cdot (3a^2+15a)}{3a^2+15a}=\frac23 \ \ \forall a \in \mathbb R \backslash \{0, -5\}$$

callculus42
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  • I got it that if I do factor out in the numerator somehow I will get the excluded value by making the denominator equal to zero but my question is that suppose if I am given the question such as find the excluded value of the expression/fraction "2/3" than is there any way to find the excluded value of expression/fraction "2/3"? – Sohaib Farooq May 13 '17 at 17:28
  • You have the equation $x\cdot (3a^2+15a)=2a^2+10a$ Now you can split the equation in two equations: $x\cdot 3a^2=2a^2$ and $x\cdot 15a=10a$. Both equations have to be fullfilled. – callculus42 May 13 '17 at 17:56