Question

Cho M = \(\left(\frac{x^2+x+10}{x^2-9}-\frac{1}{x-3}\right):\frac{1}{x-3}.\)

a) Tìm đkxđ và rút gọn M.

b) Tính M khi x = 5.

 

Answer 1

\(M=\left(\frac{x^2+x+10}{x^2-9}-\frac{1}{x-3}\right):\frac{1}{x-3}\)   \(ĐKXĐ:x\ne\pm3\)

\(M=\left[\frac{x^2+x+10}{\left(x-3\right)\left(x+3\right)}-\frac{x+3}{\left(x-3\right)\left(x+3\right)}\right]:\frac{1}{x-3}\)

\(M=\left[\frac{x^2+x+10-x-3}{\left(x-3\right)\left(x+3\right)}\right]:\frac{1}{x-3}\)

\(M=\frac{x^2+7}{\left(x-3\right)\left(x+3\right)}.\left(x-3\right)\)

\(M=\frac{x^2+7}{x+3}\)

vậy \(M=\frac{x^2+7}{x+3}\)

khi \(x=5\)thì \(M=\frac{5^2+7}{5+3}=\frac{25+7}{8}=\frac{32}{8}=4\)

vậy \(M=4\)khi \(x=5\)