Question 205624
simplify the following rational expressions:
{{{x^2-1}}}/{{{x^2-2x+1}}}
Factor whatever you can.
= (x-1)*(x+1)/((x-1)*(x-1)
Then cancel
= (x+1)/(x-1)
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{{{3x^2+7x+2}}}/{{{3x^2+13x+4}}}
= (3x+1)*(x+2)/(3x+1)*(x+4)
= (x+2)/(x+4)
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{{{-4a^2+8a-4}}}/{{{2a^2-2}}}
= -4(a-1)(a-1)/2(a-1)(a+1)
= -2(a-1)/(a+1)
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{{{3(x-2)^2+17(x-2)}}}/{{{2(x-2)^2+7(x-2)}}}
There's a temptation to cancel some things here, but you have to first expand all the terms.
= {{{(3x^2-12x+12 + 17x-34)/(2x^2-8x+8 + 7x-14)}}}
= {{{(3x^2 + 5x - 22)/(2x^2 - x - 6)}}}
= (3x + 11)(x - 2)/(2x + 3)(x - 2)
= (3x+11)/(2x+3)