1) 2a+b/4p : b+2a/8p^2 = 2a+b/4p * 8p^2/b+2a = 2p
2) 3a-2x/7x^2 : 2x-3a/14x = 3a-2x/7x^2 * 14x/2x-3a = 3a-2x / x * 2 / -(3a-2x) = -1/x * 2 = -2/x
3) a^2-3a/9y^2 : 5a/9y = a(a-3)/9y^2 * 9y/5a = a-3/y * 1/5 = a-3/5y
4) a^2+a/9b^2 : b^3/5+5a = a(a+1)/9b^2 * b^3/5+5a = a(a+1)/9 * b/5a+5 = a(a+1)/9 * b/5(a+1) = a/9 * b/5 = ab/45
5) 7ab/c^2-3c : 14ab^2/3c-9 = 7ab/c(c-3) * 3c-9/14ab^2 = 1/c(c-3) * 3(c-3)/2b = 1/c * 3/2b = 3/2bc
6) 11a/m^2-2m : 22a^2/6-3m = 11a/m(m-2) * 6-3m/22a^2 = 1/m(m-2) * -3(-2+m)/2a - 1/m * -3/2a = - 3/2am
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Answers & Comments
1) 2a+b/4p : b+2a/8p^2 = 2a+b/4p * 8p^2/b+2a = 2p
2) 3a-2x/7x^2 : 2x-3a/14x = 3a-2x/7x^2 * 14x/2x-3a = 3a-2x / x * 2 / -(3a-2x) = -1/x * 2 = -2/x
3) a^2-3a/9y^2 : 5a/9y = a(a-3)/9y^2 * 9y/5a = a-3/y * 1/5 = a-3/5y
4) a^2+a/9b^2 : b^3/5+5a = a(a+1)/9b^2 * b^3/5+5a = a(a+1)/9 * b/5a+5 = a(a+1)/9 * b/5(a+1) = a/9 * b/5 = ab/45
5) 7ab/c^2-3c : 14ab^2/3c-9 = 7ab/c(c-3) * 3c-9/14ab^2 = 1/c(c-3) * 3(c-3)/2b = 1/c * 3/2b = 3/2bc
6) 11a/m^2-2m : 22a^2/6-3m = 11a/m(m-2) * 6-3m/22a^2 = 1/m(m-2) * -3(-2+m)/2a - 1/m * -3/2a = - 3/2am