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mrredrussiap06j9h
@mrredrussiap06j9h
July 2022
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1.) (1 - x/x+1) : x/xy+y
2.) b/a + a^2-b^2/a^2 * a/a+b
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ArtemCoolAc
1.
2.
Помним, что
и что
2 votes
Thanks 5
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Answers & Comments
1.![$(1-\frac{x}{x+1}):\frac{x}{xy+y}=(\frac{x+1-x}{x+1})\cdot \frac{y(x+1)}{x}=\frac{1}{x+1}\cdot \frac{y(x+1)}{x}=\frac{y}{x} $(1-\frac{x}{x+1}):\frac{x}{xy+y}=(\frac{x+1-x}{x+1})\cdot \frac{y(x+1)}{x}=\frac{1}{x+1}\cdot \frac{y(x+1)}{x}=\frac{y}{x}](https://tex.z-dn.net/?f=%24%281-%5Cfrac%7Bx%7D%7Bx%2B1%7D%29%3A%5Cfrac%7Bx%7D%7Bxy%2By%7D%3D%28%5Cfrac%7Bx%2B1-x%7D%7Bx%2B1%7D%29%5Ccdot%20%5Cfrac%7By%28x%2B1%29%7D%7Bx%7D%3D%5Cfrac%7B1%7D%7Bx%2B1%7D%5Ccdot%20%5Cfrac%7By%28x%2B1%29%7D%7Bx%7D%3D%5Cfrac%7By%7D%7Bx%7D)
2.![$\frac{b}{a}+ \frac{a^2-b^2}{a^2}\cdot \frac{a}{a+b}=\frac{b}{a}+\frac{(a-b)(a+b)}{a^2}\cdot \frac{a}{a+b}=\frac{b}{a}+\frac{a-b}{a}=\frac{b}{a}+1-\frac{b}{a} $\frac{b}{a}+ \frac{a^2-b^2}{a^2}\cdot \frac{a}{a+b}=\frac{b}{a}+\frac{(a-b)(a+b)}{a^2}\cdot \frac{a}{a+b}=\frac{b}{a}+\frac{a-b}{a}=\frac{b}{a}+1-\frac{b}{a}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bb%7D%7Ba%7D%2B%20%5Cfrac%7Ba%5E2-b%5E2%7D%7Ba%5E2%7D%5Ccdot%20%5Cfrac%7Ba%7D%7Ba%2Bb%7D%3D%5Cfrac%7Bb%7D%7Ba%7D%2B%5Cfrac%7B%28a-b%29%28a%2Bb%29%7D%7Ba%5E2%7D%5Ccdot%20%5Cfrac%7Ba%7D%7Ba%2Bb%7D%3D%5Cfrac%7Bb%7D%7Ba%7D%2B%5Cfrac%7Ba-b%7D%7Ba%7D%3D%5Cfrac%7Bb%7D%7Ba%7D%2B1-%5Cfrac%7Bb%7D%7Ba%7D)
Помним, что![$\frac{1}{\frac{x}{y} } =\frac{y}{x} $\frac{1}{\frac{x}{y} } =\frac{y}{x}](https://tex.z-dn.net/?f=%24%5Cfrac%7B1%7D%7B%5Cfrac%7Bx%7D%7By%7D%20%7D%20%3D%5Cfrac%7By%7D%7Bx%7D)
и что![a^2-b^2=(a-b)(a+b) a^2-b^2=(a-b)(a+b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29)