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)
$frac{ {x}^{2} + 9 {y}^{2} }{x - 3y} + frac{6xy}{3y - x} = frac{ {x}^{2} + 9 {y}^{2} }{x - 3y} + frac{6xy}{ - (x - 3y)} = frac{ {x}^{2} + 9 {y}^{2} }{x - 3y} - frac{6xy}{x - 3y} = frac{ {x}^{2} + 9 {y}^{2} - 6xy }{x - 3y} = frac{ {(x - 3y)}^{2} }{x - 3y} = x - 3y$