Question

Fatore os termos das frações algébricas e depois cancele os fatores comuns.

Answer 1

$a)\\ \\ \frac{3x^{3}-9x^{2}}{x^{2}-9} =\frac{3x^{2}(x-3)}{(x+3)(x-3)} =\frac{3x^{2}}{x+3}$

$c)\\ \\ \frac{b^{2}-49}{14b^{3}-98b^{2}} =\frac{(b+7)(b-7)}{14b^{2}(b-7)} =\frac{b+7}{14b^{2}}$

$e)\\ \\ \frac{m^{4}n^{4}-1}{3m^{2}n^{2}+3} =\frac{(m^{2}n^{2}+1)(m^{2}n^{2}-1)}{3(m^{2}n^{2}+1)} =\frac{m^{2}n^{2}-1}{3}$

$b)\\ \\ \frac{a^{2}+ay}{ax+ay} =\frac{a(a+y)}{a(x+y)} =\frac{a+y}{x+y}$

$d)\\ \\ \frac{9x^{4}+24x^{2}+16}{60x^{4}b^{2}+80x^{2}b^{2}} =\frac{(3x^{2}+4)^{2}}{20x^{2}b^{2}(3x^{2}+4)} =\frac{3x^{2}+4}{20x^{2}b^{2}}$

$f)\\ \\ \frac{6x^{4}y^{5}+36x^{4}y^{7}z}{2x^{3}y^{6}+12x^{3}y^{8}z} =\frac{6x^{4}y^{5}(1+6y^{2}z)}{2x^{3}y^{6}(1+6y^{2}z)} =\frac{6x^{4}y^{5}}{2x^{3}y^{6}}$

$=\frac{3x}{y}$