# SOLUTION: <pre><b>Divide and Simplify: 5x - 7 ----------- 25x² - 49 ---------------- 5x² + 27x + 28</pre>

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 Question 43227This question is from textbook INTERMEDIATE ALGEBRA : Divide and Simplify: 5x - 7 ----------- 25x² - 49 ---------------- 5x² + 27x + 28This question is from textbook INTERMEDIATE ALGEBRA Answer by AnlytcPhil(1276)   (Show Source): You can put this solution on YOUR website!Divide and Simplify: 5x - 7 ----------- 25x² - 49 ---------------- 5x² + 27x + 28 Write it as the upper fraction divided by the the trinomial at the bottom: 5x - 7 ----------- ÷ (5x² + 27x + 28) 25x² - 49 Now put that trinomial over 1: 5x - 7 5x² + 27x + 28 ----------- ÷ ---------------- 25x² - 49 1 Now invert the second fraction and change the ÷ to × 5x - 7 1 ----------- × ---------------- 25x² - 49 5x² + 27x + 28 Factor the two denominators 5x - 7 1 ------------------ × ----------------- (5x - 7)(5x + 7) (x + 4)(5x + 7) Write as one fraction by indicating the multiplicatiom of numerators and denominators: 5x - 7 --------------------------------- (5x - 7)(5x + 7)(x + 4)(5x + 7) Cancel the (5x - 7)'s 1 5x - 7 --------------------------------- (5x - 7)(5x + 7)(x + 4)(5x + 7) 1 1 ------------------------- (5x + 7)(x + 4)(5x + 7) Since there are two factors (5x + 7) you can write their product as (5x + 7)² 1 ------------------ (x + 4)(5x + 7)² Edwin