Question

Answer 1

a) \(\dfrac{x-2}{x-1}+\dfrac{2x-1}{x-1}\)

\(=\dfrac{x-2+2x-1}{x-1}\)

\(=\dfrac{3x-3}{x-1}\)

\(=\dfrac{3\left(x-1\right)}{x-1}=3\)

b) \(\dfrac{3x-5}{3}+\dfrac{3-2x}{3}\)

\(=\dfrac{3x-5+3-2x}{3}\)

\(=\dfrac{x-2}{3}\)

Answer 2

c.

\(=\frac{10}{4b}+\frac{8b-15}{4b}=\frac{10+8b-15}{4b}=\frac{8b-5}{4b}\)

d.

\(=\frac{xy}{xy(2x-y)}+\frac{4xy}{xy(2x-y)}=\frac{xy+4xy}{xy(2x-y)}=\frac{5xy}{xy(2x-y)}=\frac{5}{2x-y}\)