Question

Please help i have know idea what to do please help and show work so i can understand thank you!

Answer 1

1.$\frac{k + 3}{4k - 2}(12k^{2} - 3})$
   $\frac{k + 3}{2(2k) - 2(1)}(3(4k^{2}) - 3(1))$
   $\frac{k + 3}{2(2k - 1)}(3(4k^{2} - 1))$
   $\frac{k + 2}{2(2k - 1)}(3(4k^{2} + 2k - 2k - 1))$
   $\frac{k + 3}{2(2k - 1)}(3(2k(2k) + 2k(1) - 1(2k) - 1(1))$
   $\frac{k + 3}{2(2k - 1)}(3(2k + 1) - 1(2k + 1))$
   $\frac{k + 3}{2(2k - 1)}(3(2k - 1)(2k + 1))$
   $\frac{3(k + 3)(2k + 1)}{2}$

2.$(\frac{x^{2} - 16}{6x})(\frac{7x}{x + 5})$
   $(\frac{x^{2} + 4x - 4x - 16}{6})(\frac{7}{x + 5})$
   $(\frac{x(x) + x(4) - 4(x) - 4(4)}{6})(\frac{7}{x + 5})$
   $(\frac{x(x + 4) - 4(x + 4)}{6})(\frac{7}{x + 5})$
   $(\frac{(x - 4)(x + 4)}{6})(\frac{7}{x + 5})$
   $\frac{7(x - 4)(x + 4)}{6(x + 5)}$

3.$(\frac{q + 5}{2})(\frac{4q}{q + 4})$
   $(\frac{q + 5}{1})(\frac{2q}{q + 4})$
   $\frac{2q(q + 5)}{q + 4}$

4.$(\frac{y^{2} - 9}{-2y})(\frac{-5y}{y + 3})$
   $(\frac{y^{2} + 3y - 3y - 9}{2})(\frac{5}{y + 3})$
   $(\frac{y(y) + y(3) - 3(y) - 3(3)}{2})(\frac{5}{y + 3})$
   $(\frac{y(y + 3) - 3(y + 3)}{2})(\frac{5}{y + 3})$
   $(\frac{(y - 3)(y + 3)}{2})(\frac{5}{y + 3})$
   $(\frac{y - 3}{2})(\frac{5}{1})$
   $\frac{5(y - 3)}{2}$

5.$\frac{8x^{2} - 20x + 15}{2x - 3}$

6.$\frac{8x^{3} - 30 + 21}{4x - 6}$
   $\frac{8x^{3} - 9}{2(2x) - 2(3)}$
   $\frac{8x^{3} - 9}{2(2x - 3)}$

7.$\frac{-10m^{9} - 12m^{6} - 4m}{2m^{4}}$
   $\frac{-10m^{9}}{2m^{4}} - \frac{12m^{6}}{2m^{4}} - \frac{4m}{2m^{4}}$
   $-5m^{5} - 6m^{2} - \frac{2}{m^{3}}$