SOLUTION: Choose the appropriate simplified expression. 1. 8x^2-10x+3/6x^2+3x-3 2. (x^2-4/x^2-1)*(x+1/x^2+2x) 3. (7/5y+25)-(4/3y+15) 4. (x^2/x^2+2x+1)/(3x/x^2-1)

Question 410099: Choose the appropriate simplified expression.
1. 8x^2-10x+3/6x^2+3x-3

2. (x^2-4/x^2-1)*(x+1/x^2+2x)

3. (7/5y+25)-(4/3y+15)

4. (x^2/x^2+2x+1)/(3x/x^2-1)

5. (2x+4/3x-3)*(12x-12/x+5)

6. (7/2xy^2)+(3/8x^2y)

7. (x^2-16/2x+8)/((x-4)^2/8x-32)

8. 5-(4x^2-5x+1/x^2-x)

9. 1/3x/5/6y

Please help me thank you!

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. 8x^2-10x+3/6x^2+3x-3
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Factor numerator and denominator:
[8x^2+4x+6x+3] / [3(2x^2+x-1)]
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= [4x(2x+1)+3(2x+1)] / [3(2x-1)(x+1)]
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= [(2x+1)(4x+3)] / [3(2x-1)(x+1)]
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2. (x^2-4/x^2-1)*(x+1/x^2+2x)
[(x-2)(x+2)/(x-1)(x+1)] * [(x+1)/x(x+2)]
--------
Cancel:
-----
=[(x-2)/(x-1)] * [1/x]
===============================

3. (7/5y+25)-(4/3y+15)
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= [7/5(y+5)] - [4/3(y+5)]
=====
least common denominator is 15*(y+5)
----
= [21/lcd] - [20/lcd]
----
= 1/[15(y+5)]
======================
Cheers,
Stan H.
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