Algebra: Factoring FractionsDate: 07/30/97 at 02:13:05 From: Wendy Herndon Subject: Algebra 2 8ab 16b2 ------ divided by --------- 4a2-b2 8a2 - 4ab My sister showed me how to do this but I couldn't understand. I think where I'm stuck is where it came to factoring. If you could help me I'd be so happy. Thanks, Wendy Date: 07/30/97 at 07:43:38 From: Doctor Anthony Subject: Re: Algebra 2 When dividing by a fraction, you can write it more clearly by MULTIPLYING by that fraction turned upside down. So the whole expression is: 8ab 8a^2 - 4ab ----------- x ------------ 4a^2 - b^2 16b^2 The term (4a^2-b^2) is a difference of squares and factorizes to (2a-b)(2a+b). You can prove this to your own satisfaction by multiplying out the two brackets: (2a-b)(2a+b) = 4a^2 + 2ab - 2ab - b^2 = 4a^2-b^2 8ab x 4a(2a - b) 32a^2.b(2a-b) ------------------ = ------------------ (2a-b)(2a+b) x 16b^2 16b^2(2a-b)(2a+b) Now you can cancel any terms that are common to the top and bottom lines. The bracket (2a-b) occurs on both lines and can be cancelled. The number 32 on the top line is reduced to 2 by the 16 on the bottom line. Also there is a factor b on both lines, and this can be cancelled. After these cancellations we get: 2a^2 --------- b(2a+b) This is as far as the simplification can be taken. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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