Question 116864
I have to express the following rational expressions in lowest terms Can you please help with the following questions. I am so confused and I don't quiet understand. There are five questions that I tried and can't get. PLEASE HELP ME!!!!
1) {{{x/((x+xy))}}}
Factor x out in the denominator, then cancel with the x in the numerator:
{{{x/(x(1+y))}}} = {{{1/((y+1))}}}
:
2){{{((3x^2+6x))/((3x^2+9x))}}}
Factor out 3x in both the numerator and denominator; cancel the 3x's
{{{(3x(x+2))/(3x(x+3))}}} = {{{(x+2)/(x+3)}}}
:
3){{{((x^2+2x+1))/((x+1))}}}
You can factor the numerator here; cancel one of the (x+1)'s leaving:
{{{((x+1)(x+1))/((x+1))}}} = x+1
:
4){{{((x^2+3x-18))/((2x-6))}}}
Factor the numerator and factor out 2 in the denominator, cancel the (x-3)'s:
{{{((x+6)(x-3))/(2(x-3))}}} = {{{((x+6))/2}}}
:
5){{{((2x^2-4x-6))/((x-3))}}}
Factor the numerator:
{{{((2x-6)(x+1))/((x-3))}}}
Notice now that we can factor (2x-6) in the numerator, then we can cancel
{{{(2(x-3)(x+1))/((x-3))}}} = 2(x+1)
:
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Study what we did here diligently, and it will all makes sense, you can email me if you have a question about it.