Question

Simplify 7x+21/x2+5x+6 divided by x+6/x+2 A. 7/x+6 B. 4x(x+7)/x+10 C. 10/x+7 D. 7/5

Answer 1

The answer is A.  And here's how you get it.  You start by simplifying between the numerator and the denominator in the top fraction. Factor the top and the botttom so you have this: [7(x+3)/(x+3)(x+2)]/[(x+6)/(x+2)].  The (x+3)'s in the top fraction cancel each other out leaving you with [7/(x+2)]/[(x+6)/(x+2)].  When you divide fractions by fractions you change the sign and flip the fraction in the denominator so now you have this: [7/(x+2)]*[(x+2)/(x+6)]. The (x+2)'s cancel each other out then leaving you with 7/(x+6)