SOLUTION: (a-5)^2/25-a^2= 25c+15d/50c^2+30d^2= 2w^2+w-6/2w+4= 4b^2-5b-6/8b^2+6b= 2y^2-9y+4/8y-2y^2= 3t^2-4tv-7v^2/t^2-v^2=

Algebra ->  Algebra  -> Numeric Fractions Calculators, Lesson and Practice  -> Lessons -> SOLUTION: (a-5)^2/25-a^2= 25c+15d/50c^2+30d^2= 2w^2+w-6/2w+4= 4b^2-5b-6/8b^2+6b= 2y^2-9y+4/8y-2y^2= 3t^2-4tv-7v^2/t^2-v^2=      Log On

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Question 189551: (a-5)^2/25-a^2=
25c+15d/50c^2+30d^2=
2w^2+w-6/2w+4=
4b^2-5b-6/8b^2+6b=
2y^2-9y+4/8y-2y^2=
3t^2-4tv-7v^2/t^2-v^2=
Answer by jim_thompson5910(21680) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first three to get you started


# 1


%28a-5%29%5E2%2F%2825-a%5E2%29 Start with the given expression.


%28%28a-5%29%28a-5%29%29%2F%2825-a%5E2%29 Expand


%28%28a-5%29%28a-5%29%29%2F%28-%28a%2B5%29%28a-5%29%29 Factor the denominator


-%28%28a-5%29%28a-5%29%29%2F%28%28a%2B5%29%28a-5%29%29 Reduce


-%28%28a-5%29highlight%28%28a-5%29%29%29%2F%28%28a%2B5%29highlight%28%28a-5%29%29%29 Highlight the common terms.


-%28%28a-5%29cross%28%28a-5%29%29%29%2F%28%28a%2B5%29cross%28%28a-5%29%29%29 Cancel out the common terms.


-%28a-5%29%2F%28a%2B5%29 Simplify


So %28a-5%29%5E2%2F%2825-a%5E2%29=-%28a-5%29%2F%28a%2B5%29 where a%3C%3E-5 or a%3C%3E5



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# 2


%2825c%2B15d%29%2F%2850c%5E2%2B30d%5E2%29 Start with the given expression.


%285%285c%2B3d%29%29%2F%2850c%5E2%2B30d%5E2%29 Factor 25c%2B15d to get 5%285c%2B3d%29.


%285%285c%2B3d%29%29%2F%285%2810c%5E2%2B6d%5E2%29%29 Factor 50c%5E2%2B30d%5E2 to get 5%2810c%5E2%2B6d%5E2%29.


%28highlight%285%29%285c%2B3d%29%29%2F%28highlight%285%29%2810c%5E2%2B6d%5E2%29%29 Highlight the common terms.


%28cross%285%29%285c%2B3d%29%29%2F%28cross%285%29%2810c%5E2%2B6d%5E2%29%29 Cancel out the common terms.


%285c%2B3d%29%2F%2810c%5E2%2B6d%5E2%29 Simplify.


So %2825c%2B15d%29%2F%2850c%5E2%2B30d%5E2%29=%285c%2B3d%29%2F%2810c%5E2%2B6d%5E2%29



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# 3


%282w%5E2%2Bw-6%29%2F%282w%2B4%29 Start with the given expression.


%28%28w%2B2%29%282w-3%29%29%2F%282w%2B4%29 Factor 2w%5E2%2Bw-6 to get %28w%2B2%29%282w-3%29.


%28%28w%2B2%29%282w-3%29%29%2F%282%28w%2B2%29%29 Factor 2w%2B4 to get 2%28w%2B2%29.


%28highlight%28%28w%2B2%29%29%282w-3%29%29%2F%282%2Ahighlight%28%28w%2B2%29%29%29 Highlight the common terms.


%28cross%28%28w%2B2%29%29%282w-3%29%29%2F%282%2Across%28%28w%2B2%29%29%29 Cancel out the common terms.


%282w-3%29%2F2 Simplify.


So %282w%5E2%2Bw-6%29%2F%282w%2B4%29 simplifies to %282w-3%29%2F2.


In other words, %282w%5E2%2Bw-6%29%2F%282w%2B4%29=%282w-3%29%2F2 where w%3C%3E-2