SOLUTION: I am currently taking Intermediate Algebra, I am having problems with rational expressions. Simplify rational expression 1. x-2/8x^2-32 Multiply Rational Expression 2. 8x^2

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Question 315710: I am currently taking Intermediate Algebra, I am having problems with rational expressions.
Simplify rational expression
1. x-2/8x^2-32
Multiply Rational Expression
2. 8x^2/x^2-9*x^2+6x+9/16x^3
Divide Rational Expression
3. 3y+12/8y^3/9y+36/16y^3
Add Rational Expression
4. 7/x^2-x-6+5/x-3
Subract Rational Expression
5. 3x/x^2+3x-10-2x/x^2+x-6

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Simplify rational expression
1. x-2/8x^2-32
(x-2)/[8(x^2-4)]
(x-2)/[8(x-2)(x+2)]
= 1/[8(x+2)]
------------------------
Multiply Rational Expression
2. [8x^2/x^2-9]
Factor:
[8x^2/(x-3)(x+3)]
Cancel where you can:
= [1/(x-3)]
= (x+3)/[2x(x-3)]
------------------------------
Divide Rational Expression
3. [3y+12/8y^3]/[9y+36/16y^3]
[3(y+4)/8y^3] / [9(y+4)/16y^3]
Invert the denominator and multiply:
[3(y+4)/8y^3] * [16y^3/[9(y+4)]]
Cancel where you can:
[1/1] * [2/[3]]
= 2/3
========

Add Rational Expression
4. 7/x^2-x-6+5/x-3
[7/(x-3)(x+2)] + [5/(x-3)]
lcd = (x-3)(x+2)
7/lcd + 5(x+2)/lcd
[7+5x+10)/lcd
[5x+17]/[(x-3)(x+2)]
==========================
Subract Rational Expression
5. 3x/x^2+3x-10-2x/x^2+x-6
[3x/(x+5)(x-2)] - [2x/(x+3)(x-2)]
lcd = (x+5)(x-2)(x+3)
---
= [3x(x+3)]/lcd - [2x(x+5)]/lcd
---
= [3x^2+9x-(2x^2+10x)]/lcd
---
= [x^2-x]/[(x+5)(x-2)(x+3)]
===============================
Cheers,
Stan H.