Rational Expressions: (9x^2 - 4y^2)/(3x^2 - 2xy), etc.

[lydia2468]

How do you do these questions?

a) (9x² - 4y²) / (3x² - 2xy)

b) 2x/(x + 5) = 2 - 4x/[(x+5)(x+1)]

Also, when I reduced/simplified this question:

c) (7x² - 21x) / (7x² - 28x + 21)

When I reduced (simplified) this expression, I got:

[7x(x - 3)] / [(x - 21)(x - 7)]

The problem is, I don't know what to do after that step.

Thanks in advance!!
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Edited by stapel -- Reason for edit: clarity of formatting.

 

[stapel]

a) I will guess that the instructions are to "simplify". For the numerator, apply the difference-of-squares formula you've memorized. For the denominator, just factor out the common factor. Then cancel the common factor to get the simplified form.

b) I will guess that the instructions are to "solve". A good first step would be to multiply through by the common denominator of (x + 5)(x + 1). Then solve the resulting quadratic equation by the usual methods. Remember to check your solutions in the original equation, to make sure that they don't cause division by zero.

c) I will guess that you factored the 7 from the numerator and denominator, and cancelled, to get:

. . . . .\(\displaystyle \L \frac{x^2\,-\,3x}{x^2\,-\,4x\,+\,3}\)

How did you get that x² - 4x + 3 equals (x - 21)(x - 7) = x² - 28x + 147?

Please reply showing all of your steps. Thank you.

Eliz.

 

[lydia2468]

a) ya i want to simplify and reduce the rational expression. but like since 9 and 4 dont have a common factor do this?
xy(9x-4y)

and for the bottom part.
x(3x-2y)
????

for c. You were right I made a mistake. thanksss

 

[stapel]

a) [Yes, I] want to simplify and reduce the rational expression. [But] since 9 and 4 [don't] have a common factor[, should I] do this?
xy(9x-4y)

Since xy(9x - 4y) equals 9x²y - 4xy², which is not what you started with, this would not be the way to factor. Instead, try using the difference-of-squares formula you've memorized:

. . . . .m² - n² = (m - n)(m + n)

and for the bottom part.
x(3x-2y)

Yes. Once you factor the numerator correctly, you can continue with the instructions: cancel off the common factor to get the simplified answer.

Eliz.