Question

Thực hiện phép tính :

a) \(\frac{3x-2}{2xy}\)-\(\frac{7x-4}{2xy}\)

b) \(\frac{6}{x^2+4x}+\frac{3}{2x+8}\)

c) \(\frac{8xy}{3x-1}:\frac{12xy^3}{5-15x}\)

d) \(\frac{x^2}{x^2-4x+4}\) . \(\frac{2x-4}{4x}\)

Answer 1

a) \(\frac{3x-2}{2xy}-\frac{7x-4}{2xy}\)

\(=\frac{3x-2}{2xy}+\frac{-\left(7x-4\right)}{2xy}\)

\(=\frac{3x-2-7x+4}{2xy}\)

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

\(=\frac{2.\left(-2x+1\right)}{2xy}.\)

\(=\frac{-2x+1}{xy}.\)

b) \(\frac{6}{x^2+4x}+\frac{3}{2x+8}\)

Ta có:

\(x^2+4x=x.\left(x+4\right)\)

\(2x+8=2.\left(x+4\right)\)

\(MTC:2x.\left(x+4\right)\)

\(\frac{6}{x^2+4x}+\frac{3}{2x+8}\)

\(=\frac{6}{x.\left(x+4\right)}+\frac{3}{2.\left(x+4\right)}\)

\(=\frac{6.2}{2x.\left(x+4\right)}+\frac{3x}{2x.\left(x+4\right)}\)

\(=\frac{12}{2x.\left(x+4\right)}+\frac{3x}{2x.\left(x+4\right)}\)

\(=\frac{12+3x}{2x.\left(x+4\right)}\)

\(=\frac{3.\left(4+x\right)}{2x.\left(x+4\right)}\)

\(=\frac{3.\left(x+4\right)}{2x.\left(x+4\right)}\)

\(=\frac{3}{2x}.\)

Chúc bạn học tốt!