Question

Виконайте дії будь ласка

Answer 1

$\displaystyle 1)\frac{4}{b}+\frac{7}{b+2} =\frac{4(b+2)}{b(b+2)} +\frac{7b}{b(b+2)} =\frac{4b+8+7b}{b(b+2)}=\frac{11b+8}{b^{2}+2b }$

$\displaystyle 2) \frac{3}{m-n}-\frac{2}{m+n} =\frac{3(m+n)}{(m-n)(m+n)} -\frac{2(m-n)}{(m-n)(m+n)} =\frac{3m+3n}{(m-n)(m+n)}-\frac{2m-2n}{(m-n)(m+n)} =\frac{3m+3n-(2m-2n)}{(m-n)(m+n)}=\frac{3m+3n-2m+2n}{(m-n)(m+n)}=\frac{m+5n}{m^{2}-n^{2} }$

$\displaystyle 3) \frac{p}{p-2} -\frac{3}{p+3}=\frac{p(p+3)}{(p-2)(p+3)} -\frac{3(p-2)}{(p-2)(p+3)} =\frac{p^{2}+3p }{(p-2)(p+3)} -\frac{3p-6}{(p-2)(p+3)} =\frac{p^{2} +3p-3p+6}{(p-2)(p+3)} =\frac{p^{2} +6}{p^{2}+3p-2p-6 } =\frac{p^{2} +6}{p^{2}+p-6 }$

$\displaystyle4)\frac{x}{1-x} +\frac{1+x}{x} =\frac{x^{2} }{x(1-x)} +\frac{(1+x)(1-x)}{x(1-x)} =\frac{x^{2}+(1-x+x-x^{2} ) }{x(1-x)}=\frac{1}{x-x^{2} }$