Question

Выполните вычитание:
1) a-5/5a^3 - 1-a/a^4
2) 9/a - 18/a^2+2a
3) x^2/x^2-49 - x/x+7
4) 7b - 21b^2/3b+4

Answer 1

Объяснение:

$\tt\displaystyle \frac{a-5}{5a^3}-\frac{1-a}{a^4} =\frac{a(a-5)-5(1-a)}{5a^4}=\frac{a^2-5a-5+5a}{5a^4} =\bold{\frac{a^2-5}{5a^4} }$

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$\tt\displaystyle \frac{9}{a}-\frac{18}{a^2+2a} =\frac{9}{a}-\frac{18}{a(a+2)} =\frac{9(a+2)-18}{a(a+2)} =\\\\\\=\frac{9a+18-18}{a(a+2)} =\frac{9a}{a(a+2)} =\bold{\frac{9}{a+2} }$

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$\tt\displaystyle \frac{x^2}{x^2-49} -\frac{x}{x+7} =\frac{x^2}{(x-7)(x+7)} -\frac{x}{x+7} =\frac{x^2-x(x-7)}{(x-7)(x+7)} =\\\\\\=\frac{x^2-x^2+7x}{(x-7)(x+7)} =\bold{\frac{7x}{x^2-49} }$

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$\tt\displaystyle 7b-\frac{21b^2}{3b+4} =\frac{7b(3b+4)-21b^2}{3b+4} =\frac{21b^2+28b-21b^2}{3b+4}=\bold{ \frac{28b}{3b+4}}$