Question

Tìm x để A nguyên

a)A= \(\frac{4x-5}{x+1}\)

b) A= \(\frac{7x-3}{2x+1}\)

Answer 1

a) Để A là số nguyên \(\Leftrightarrow\frac{4x-5}{x+1}\in Z\)

\(\Leftrightarrow4x-5⋮x+1\)

Ta có : \(x+1⋮x+1\Rightarrow4x+4⋮x+1\)

\(\Rightarrow4x-5-4x-4⋮x+1\)

\(\Rightarrow-9⋮x+1\Leftrightarrow x+1\inƯ\left(-9\right)=\left\{\pm1,\pm3,\pm9\right\}\)

\(\Rightarrow x\in\left\{-2,0,-4,2,-10,8\right\}\)

Vậy : \(x\in\left\{-2,0,-4,2,-10,8\right\}\)

Answer 2

b) Để A là số nguyên \(\Leftrightarrow\frac{7x-3}{2x+1}\in Z\)

\(\Leftrightarrow7x-3⋮2x+1\)

\(\Leftrightarrow14x-6⋮2x+1\)

\(\Leftrightarrow14x-6-14x-7⋮2x+1\)

\(\Leftrightarrow-13⋮2x+1\Leftrightarrow2x+1\inƯ\left(-13\right)=\left\{\pm1,\pm13\right\}\)

\(\Leftrightarrow2x\in\left\{-2,0,-14,12\right\}\)

\(\Leftrightarrow x\in\left\{-1,0,-7,-6\right\}\)