Need help with simplifying rational expressions

I can't figure out how to do these; can someone run me through the process? And please, pretend you're explaining to someone who's a complete and utter dunce when it comes to math.

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Simplify the rational expression:

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Factor out the coefficients of *x on the numerator and denominator of the rational expression: *

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Simplify the rational expression:

*t*^{2} + 3*t* − 18 |

*t*^{2} − 12*t* + 27 |

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Simplify the rational expression.

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These were the ones I was having the most trouble on. I'm not asking you to do all of them for me (though feel free if you want;)), I just need to have it slowly explained how.

Re: Need help with simplifying rational expressions

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Originally Posted by

**InDrk** I can't figure out how to do these; can someone run me through the process? And please, pretend you're explaining to someone who's a complete and utter dunce when it comes to math.

There would be no point in trying to explain to a "complete and utter dunce". I would prefer to assume an intelligent person who has little background in algebra.

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Simplify the rational expression:

I presume you know that (as long as ).

95= 5(19) and 35= 5(7) is

so

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Factor out the coefficients of *x on the numerator and denominator of the rational expression: *

Okay, the "coefficient of x" in the numerator is -1 and 2= (-1)(-2). 2- x= -2(-1)+ x(-1)= -1(-2+ x)= -1(x- 2). The coefficient of x in the denominator 5: 5x- 10= 5(x-2). So, as long as x is not 2, we cancel the "x- 2" in numerator and denominator. That is which could also be written as .

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Simplify the rational expression:

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*t*^{2} + 3*t* − 18 |

*t*^{2} − 12*t* + 27 |

Start by trying to factor. 18= 2(3)(3) can be factored with two factors as either 2(9) or 6(3). 9- 2= 7, not 3 but 6- 3= 3. So ) can be factored with two factors are 3(9) and 9+ 3= 12! So . So the fraction is . Now you can cancel the two "t- 3" terms.

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Simplify the rational expression.

The denominator is (x- 2)+ 5= x+ 3 which has no factors in common with x- 2. So we cannot cancel anything and only have

as the simplest form.

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These were the ones I was having the most trouble on. I'm not asking you to do all of them for me (though feel free if you want;)), I just need to have it slowly explained how.