Question

Привести дроби к общему знаменателю:
1) 7/(x-y)² и 5/x-y
2) 5c/(c-2)² и 6/c-2
3) 7a/3x-y и 6b/3x+y
4) 3x/4x+4y и x/8x+8y
5) 2m/(m-n)³ и 2n/(m-n)² и 1/m²-n²
6) 3a/2a-3 и 4a/2a+3 и 5b/4a²c-9c​

Answer 1

1)

$\frac{7}{(x-y)^2} \quad \frac{5}{x-y}\\\\\frac{7}{(x-y)^2} \quad \frac{5(x-y)}{(x-y)^2}$

2)

$\frac{5c}{(c-2)^2} \quad \frac{6}{c-2}\\\\\frac{5c}{(c-2)^2} \quad \frac{6(c-2)}{(c-2)^2}$

3)

$\frac{7a}{3x-y} \quad \frac{6b}{3x+y}\\\\\frac{7a\left(3x+y\right)}{\left(3x-y\right)\left(3x+y\right)}\quad \frac{6b\left(3x-y\right)}{\left(3x+y\right)\left(3x-y\right)}$

4)

$\frac{3x}{4x+4y} \quad \frac{x}{8x+8y}\\\\\frac{3x}{4\left(x+y\right)} \quad \frac{x}{8\left(x+y\right)}\\\\\frac{6x}{8\left(x+y\right)}\quad \frac{x}{8\left(x+y\right)}$

5)

$\frac{2m}{(m-n)^3} \quad \frac{2n}{(m-n)^2} \quad \frac{1}{m^2-n^2} \\\\\frac{2m}{\left(m-n\right)^3}\quad\frac{2n}{\left(m-n\right)^2}\quad\frac{1}{\left(m+n\right)\left(m-n\right)}\\\\\frac{2m\left(m+n\right)}{\left(m-n\right)^3\left(m+n\right)}+\frac{2n\left(m-n\right)\left(m+n\right)}{\left(m-n\right)^3\left(m+n\right)}+\frac{\left(m-n\right)^2}{\left(m-n\right)^3\left(m+n\right)}$

6)

$\frac{3a}{2a-3} \quad \frac{4a}{2a+3} \quad \frac{5b}{4a^2c-9c} \\\\\frac{3a}{2a-3}\quad \frac{4a}{2a+3}\quad\frac{5b}{c\left(2a+3\right)\left(2a-3\right)}\\\\\frac{3ac\left(2a+3\right)}{\left(2a-3\right)c\left(2a+3\right)}\quad\frac{4ac\left(2a-3\right)}{\left(2a+3\right)c\left(2a-3\right)}\quad\frac{5b}{c\left(2a-3\right)\left(2a+3\right)}$