Question

1)x/y-1 + 2/1-y=?
2)3c/c-d + 3d/d-c=?
3)3m+2n/2m-3n - m-8n/3n-2m=?
4)b²/2b-14 + 49/14-2b=?

Answer 1

$\frac{x}{y - 1} + \frac{2}{1 - y} = \frac{x}{y - 1} - \frac{2}{y - 1} = \frac{x - 2}{y - 1}$

$\frac{3c}{c - d} + \frac{3d}{d - c} = \frac{3c}{c - d} - \frac{3d}{c - d} = \frac{3c - 3d}{c - d} = \frac{3(c - d)}{c - d} = 3$

$\frac{3m + 2n}{2m - 3n} - \frac{m - 8n}{3n - 2m} = \frac{3m + 2n}{2m - 3n} + \frac{m - 8n}{2m - 3n} = \frac{3m + 2n + m - 8n}{2m - 3n} = \frac{4m - 6n}{2m - 3n} = \frac{2(2m - 3n)}{2m - 3n} = 2$

$\frac{ {b}^{2} }{2b - 14} + \frac{49}{14 - 2b} = \frac{ {b}^{2} }{2b - 14} - \frac{49}{2b - 14} = \frac{ {b}^{2} - 49}{2b - 14} = \frac{(b - 7)(b + 7)}{2(b - 7)} = \frac{b + 7}{2}$