Question

упростите выражения:
1)x/y-1+5/1-y
2)a/c-3-6/3-c
3)2m/m-n+2n/n-m
4)5p/2q-p+10q/p-2q
5)a^2+16/a-4+8a/4-a
6)x^2+9y^2/x-3y+6xy/3y-x

Answer 1

1)
$\frac{x}{y - 1} + \frac{5}{1 - y} = \frac{x}{y - 1} + \frac{5}{ - (y - 1)} = \frac{x}{y - 1} - \frac{5}{y - 1} = \frac{x - 5}{y - 1}$
2)
$\frac{a}{c - 3} - \frac{6}{3 - c} = \frac{a}{c - 3} - \frac{6}{ - (c - 3)} = \frac{a}{c - 3} + \frac{6}{c - 3} = \frac{a + 6}{c - 3}$
3)
$\frac{2m}{m - n} + \frac{2n}{n - m} = \frac{2m}{m - n} + \frac{2n}{ - (m - n)} = \frac{2m}{m - n} - \frac{2n}{m - n} = \frac{2m - 2n}{m - n} = \frac{2(m - n)}{m - n} = 2$
4)
$\frac{5p}{2q - p} + \frac{10q}{p - 2q} = \frac{5p}{2q - p} + \frac{10q}{ - (2q - p)} = \frac{5p}{2q - p} - \frac{10q}{2q - p} = \frac{5p - 10q}{2q - p} = \frac{5(p - 2q)}{2q - p} = \frac{ - 5(2q - p)}{2q - p} = - 5$
5)
$\frac{ {a}^{2} + 16}{a - 4} + \frac{8a}{4 - a} = \frac{{a}^{2} + 16}{a - 4} + \frac{8a}{ - (a - 4)} = \frac{{a}^{2} + 16}{a - 4} - \frac{8a}{a - 4} = \frac{ {a}^{2} + 16 - 8a}{a - 4} = \frac{ {(a - 4)}^{2} }{a - 4} = a - 4$
6)
$\frac{ {x}^{2} + 9 {y}^{2} }{x - 3y} + \frac{6xy}{3y - x} = \frac{ {x}^{2} + 9 {y}^{2} }{x - 3y} + \frac{6xy}{ - (x - 3y)} = \frac{ {x}^{2} + 9 {y}^{2} }{x - 3y} - \frac{6xy}{x - 3y} = \frac{ {x}^{2} + 9 {y}^{2} - 6xy }{x - 3y} = \frac{ {(x - 3y)}^{2} }{x - 3y} = x - 3y$