# номер 121 гдз 8 класс алгебра Муравин Муравин

1)$$\frac{x-a}{x-b}, x=\frac{ab}{a+b}$$ $$\frac{\frac{ab}{a+b}-a}{\frac{ab}{a+b}-b}$$ 1)$$\frac{ab}{a+b}-a=\frac{ab-a^{2}-ab}{a+b}=$$ $$=-\frac{a^{2}}{a+b}$$ 2)$$\frac{ab}{a+b}-b=\frac{ab-ab-b^{2}}{a+b}=$$ $$=-\frac{b^{2}}{a+b}$$ 3)$$-\frac{a^{2}}{a+b}:\left ( -\frac{b^{2}}{a+b} \right )=$$ $$=\frac{a^{2}}{a+b}\cdot \frac{a+b}{b^{2}}=\frac{a^{2}}{b^{2}}$$ 2)$$\frac{a^{2}-abx}{b^{2}+abx}, x=\frac{a-b}{a+b}$$ $$\frac{a^{2}-ba\cdot \frac{a-b}{a+b}}{b^{2}+ab\cdot \frac{a-b}{a+b}}$$ 1)$$a^{2}-ab\frac{\left ( a-b \right )}{a+b}=$$ $$=\frac{a^{3}+a^{2}b-a^{2}b+ab^{2}}{a+b}=$$ $$=\frac{a^{3}+ab^{2}}{a+b}=\frac{a\left ( a^{2}+b^{2} \right )}{a+b}$$ 2)$$b^{2}+ab\cdot \frac{\left ( a-b \right )}{a+b}=$$ $$=\frac{ab^{2}+b^{3}+a^{2}b-ab^{2}}{a+b}=$$ $$=\frac{b\left ( b^{2}+a^{2} \right )}{a+b}$$ 3)$$\frac{a\left ( a^{2}+b^{2} \right )}{a+b}:\frac{b\left ( b^{2}+a^{2} \right )}{a+b}=$$ $$=\frac{a\left ( a^{2}+b^{2} \right )}{a+b}\cdot \frac{a+b}{b\left ( b^{2}+a^{2} \right )}=\frac{a}{b}$$ 3)$$\frac{ax}{x-a}-\frac{bx}{x-b}, x=\frac{ab}{a+b}$$ $$\frac{a\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-a}-\frac{b\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-b}$$ 1)$$\frac{a^{2}b}{a+b}:\frac{ab-a^{2}-ab}{a+b}=$$ $$=\frac{a^{2}b}{a+b}\cdot -\frac{a+b}{a^{2}}=-b$$ 2)$$\frac{ab^{2}}{a+b}:\frac{ab-ab-b^{2}}{a+b}=$$ $$=\frac{ab^{2}\left ( a+b \right )}{\left ( a+b \right )\left ( -b^{2} \right )}=-a$$
3) -b - (-a) = a - b
4)$$\frac{bx}{x-a}+\frac{ax}{x-b}, x=\frac{ab}{a+b}$$ $$\frac{b\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-a}+\frac{a\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-b}$$ 1)$$\frac{ab^{2}}{a+b}:\frac{ab-a^{2}-ab}{a+b}=$$ $$=\frac{ab^{2}}{a+b}\cdot \frac{a+b}{-a^{2}}=\frac{-b^{2}}{a}$$ 2)$$\frac{a^{2}b}{a+b}:\frac{ab-ab-b^{2}}{a+b}=$$ $$=\frac{a^{2}b}{a+b}\cdot \frac{a+b}{-b^{2}}=\frac{-a^{2}}{b}$$ 3)$$-\frac{b^{2}}{a}+\left ( -\frac{a^{2}}{b} \right )=$$ $$=-\frac{b^{2}}{a}-\frac{a^{2}}{b}=\frac{-b^{3}-a^{3}}{ab}=$$ $$=-\frac{a^{3}+b^{3}}{ab}$$