Question

Cho biểu thức: B = \(\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x.\left(x+5\right)}\)

a) Tìm đkxđ của B

b) Tìm x để B = 0; B = \(\frac{1}{4}\)

Answer 1

Lời giải:

a) ĐKXĐ:

\(\left\{\begin{matrix} 2x+10\neq 0\\ x\neq 0\\ 2x(x+5)\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\neq -5\\ x\neq 0\end{matrix}\right.\)

b)

\(B=\frac{x(x^2+2x)}{x(2x+10)}+\frac{(2x+10)(x-5)}{x(2x+10)}+\frac{50-5x}{x(2x+10)}\)

\(=\frac{x^3+2x^2+2(x^2-25)+50-5x}{x(2x+10)}=\frac{x^3+4x^2-5x}{2x(x+5)}=\frac{x^2+4x-5}{2(x+5)}=\frac{(x-1)(x+5)}{2(x+5)}=\frac{x-1}{2}\)

Để $B=0\Leftrightarrow \frac{x-1}{2}=0\Leftrightarrow x=1$ (thỏa mãn)

Để $B=\frac{1}{4}\Leftrightarrow \frac{x-1}{2}=\frac{1}{4}$

$\Leftrightarrow x-1=\frac{1}{2}\Leftrightarrow x=\frac{3}{2}$ (thỏa mãn)

Answer 2

Lời giải:

a) ĐKXĐ:

\(\left\{\begin{matrix} 2x+10\neq 0\\ x\neq 0\\ 2x(x+5)\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\neq -5\\ x\neq 0\end{matrix}\right.\)

b)

\(B=\frac{x(x^2+2x)}{x(2x+10)}+\frac{(2x+10)(x-5)}{x(2x+10)}+\frac{50-5x}{x(2x+10)}\)

\(=\frac{x^3+2x^2+2(x^2-25)+50-5x}{x(2x+10)}=\frac{x^3+4x^2-5x}{2x(x+5)}=\frac{x^2+4x-5}{2(x+5)}=\frac{(x-1)(x+5)}{2(x+5)}=\frac{x-1}{2}\)

Để $B=0\Leftrightarrow \frac{x-1}{2}=0\Leftrightarrow x=1$ (thỏa mãn)

Để $B=\frac{1}{4}\Leftrightarrow \frac{x-1}{2}=\frac{1}{4}$

$\Leftrightarrow x-1=\frac{1}{2}\Leftrightarrow x=\frac{3}{2}$ (thỏa mãn)