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Question 576266: Needing some help with rational expressions. Not quite sure how to solve these.
1) Add. Simplify if possible. ((x^2+17x)/(x^2-9x)) + ((x^2-6x)/(x^2-9x))
2) Find all numbers for which the rational expression is undefined. (t^3-8t)/(t^2-25). Indicate if the expression is defined for every real number.
3) Subtract. Simplify if possible. (a/(v+a)) - (a/(v-a))
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 1) Add. Simplify if possible. ((x^2+17x)/(x^2-9x)) + ((x^2-6x)/(x^2-9x))
(x^2+17x)/(x^2-9x)) + ((x^2-6x)/(x^2-9x)
(x^2+17x+x^2-6x/(x^2-9x)
(2x^2+17x-6x/(x^2-9x)
(2x^2+11x)/(x^2-9x)
(x(2x+11))/(x(x-9))
(2x+11)/(x-9)
.
2) Find all numbers for which the rational expression is undefined. (t^3-8t)/(t^2-25). Indicate if the expression is defined for every real number.
It is undefined if the denominator is zero.
so, set
t^2-25=0
t^2-5^2=0
(t-5)(t+5) = 0
t = {-5, 5} (numbers where expression is undefined)
.
So, expression is NOT defined for every real number
.
3) Subtract. Simplify if possible. (a/(v+a)) - (a/(v-a))
(a/(v+a)) - (a/(v-a))
(a(v-a)/(v+a)(v-a)) - (a(v+a)/(v+a)(v-a))
(a(v-a) - a(v+a))/((v+a)(v-a))
(av-a^2 - av-a^2)/((v+a)(v-a))
(-a^2-a^2)/((v+a)(v-a))
(-2a^2)/((v+a)(v-a))
(2a^2)/((v+a)(a-v))
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