SOLUTION: Hi, Please help me to solve step-by-step on these questions. Thank you very much. 5. Explain what we must do to simplify and reduce the rational expression. Than solve the step

Question 1112495: Hi,
Please help me to solve step-by-step on these questions.
Thank you very much.
5. Explain what we must do to simplify and reduce the rational expression. Than solve the steps to reduce it to lowest terms.
(10x -15y)/(6y -4x)
6. Perform the indicated operation. Show the steps in factoring and reducing the answers to lowest terms.
(8x^3-27y^3)/(6y -4x^2+2xy-15y^2) + (9y^2-4x^2)/(2x^2-3xy-9y^2)

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Explain what we must do to simplify and reduce the rational expression. Than solve the steps to reduce it to lowest terms.
(10x -15y)/(6y -4x)
= -(10x -15y)/(4x - 6y)
Divide the NUM by 5 and the DEN by 2
=========================
6. Perform the indicated operation. Show the steps in factoring and reducing the answers to lowest terms.
(8x^3-27y^3)/(6y -4x^2+2xy-15y^2) + (9y^2-4x^2)/(2x^2-3xy-9y^2)
------
= (8x^3-27y^3)/(6y -4x^2+2xy-15y^2) + (9y^2-4x^2)/(2x^2-3xy-9y^2)
Factoring is not always obvious, but you learn nothing by having someone else do it.
Try it.
email via the TY note for help or to check you work.
===============
Hint: (8x^3-27y^3) is a difference of 2 cubes.
a^3 - b^3 = (a-b)*(a^2 + ab + b^2)
----
(9y^2 - 4x^2) is a difference of 2 squares.

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