solve 3m^2-75/6m^2+30m/4m-20/9m^2+45m

Question

chapter 8, section 8.3-8.6

Answer 1

3m²-75=3(m-5)(m+5); 6m²+30m=6m(m+5); 4m-20=4(m-5); 9m²+45m=9m(m+5).

Let A=3(m-5)(m+5), B=6m(m+5), C=4(m-5), D=9m(m+5).

A/B/C/D=(A/B)/(C/D); A/B=(m-5)/2m; C/D=4(m-5)/9m(m+5);

(A/B)/(C/D)=(A/B)(D/C)=((m-5)/2m)(9m(m+5))/(4(m-5))=

9m(m+5)/8m=9(m+5)/8.

CHECK

Let m=11, then the final result should be 9(16)/8=18.

A=288, B=1056, C=24, D=1584; (288/1056)/(24/1584)=(3/11)/(1/66)=66(3/11)=18. This seems to confirm the solution: 9(m+5)/8.