SOLUTION: How do I solve the following rational expressions and express the results in the lowest terms: 1. 14z^3/15y^3*10z^2/4y 2. 7v^4w^5/16u*5v^2/8u^4v^6 3. u^2+16u+63/u+7*1/u+9

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I solve the following rational expressions and express the results in the lowest terms: 1. 14z^3/15y^3*10z^2/4y 2. 7v^4w^5/16u*5v^2/8u^4v^6 3. u^2+16u+63/u+7*1/u+9       Log On


   

Question 173954: How do I solve the following rational expressions and express the results in the lowest terms:
1. 14z^3/15y^3*10z^2/4y
2. 7v^4w^5/16u*5v^2/8u^4v^6
3. u^2+16u+63/u+7*1/u+9
4. 24x^3z^2/6y^2/8xz^4/3y^4
5. z^2-10z+21/z^2-13z+36/z^2-11z+24/z^2-9z+14
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
1. %28%2814z%5E3%29%2F%2815y%5E3%29%29%2A%2810z%5E2%2F4y%29 Multiply the numerators and the denominators.
%28140z%5E5%29%2F%2860y%5E4%29 Reduce the numerical part of the fraction.
highlight%287z%5E5%2F3y%5E4%29
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2. %28%287v%5E4w%5E5%29%2F%2816u%29%29%2A%28%285v%5E2%29%2F%288u%5E4v%5E6%29%29 Multiply the numerators and the denominators.
%2835cross%28v%5E6%29w%5E5%29%2F%28128u%5E5cross%28v%5E6%29%29 Cancel the indicated factors.
highlight%28%2835w%5E5%29%2F%28128u%5E5%29%29
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3. %28%28u%5E2%2B16u%2B63%29%2F%28u%2B7%29%29%2A%281%2F%28u%2B9%29%29 Multiply the numerators and the denominators.
%28u%5E2%2B16u%2B63%29%2F%28%28u%2B7%29%28u%2B9%29%29 Multiply the factors in the denominator.
cross%28u%5E2%2B16u%2B63%29%2Fcross%28u%5E2%2B16u%2B63%29=highlight%281%29
---------------------
4. %28%2824x%5E3z%5E2%29%2F%286y%5E2%29%29%2F%28%288xz%5E4%29%2F%283y%5E4%29%29 Invert the lower fraction and multiply.
%28%2824x%5E3z%5E2%29%2F%286y%5E2%29%29%2A%28%283y%5E4%29%2F%288xz%5E4%29%29 Multiply the numerators and the denominators.
%2872x%5E3y%5E4z%5E2%29%2F%2848xy%5E2z%5E4%29 Reduce the numerical part of the fraction.
%283x%5E3y%5E4z%5E2%29%2F%282xy%5E2z%5E4%29 Factor the variables.
Cancel the indicated factors.
highlight%28%283x%5E2y%5E2%29%2F%282z%5E2%29%29
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5. Invert the lower fraction and multiply.
Before multiplying, factor the numerators and the denominators.
Cancel the indicated factors.
%28%28z-7%29%2F%28%28z-4%29%28z-9%29%29%29%2A%28%28%28z-2%29%28z-7%29%29%2F%28z-8%29%29%29
%28%28z-7%29%28z-2%29%28z-7%29%29%2F%28%28z-4%29%28z-9%29%28z-8%29%29 Multiply the numerators and the denominators.
highlight%28%28z%5E3-16z%5E2%2B77z-98%29%2F%28z%5E3-21z%5E2%2B140z-288%29%29