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)

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

4)

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

5)

$frac{2m}{(m-n)^3} quad frac{2n}{(m-n)^2} quad frac{1}{m^2-n^2} \\frac{2m}{left(m-nright)^3}quadfrac{2n}{left(m-nright)^2}quadfrac{1}{left(m+nright)left(m-nright)}\\frac{2mleft(m+nright)}{left(m-nright)^3left(m+nright)}+frac{2nleft(m-nright)left(m+nright)}{left(m-nright)^3left(m+nright)}+frac{left(m-nright)^2}{left(m-nright)^3left(m+nright)}$

6)

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