Bài 14:
a: ĐKXĐ: \(a\notin\left\{3;-3;-1\right\}\)
\(A=\left(\dfrac{2a}{a+3}-\dfrac{a}{3-a}-\dfrac{3a^2+3}{a^2-9}\right):\dfrac{a+1}{a-3}\)
\(=\left(\dfrac{2a}{a+3}+\dfrac{a}{a-3}-\dfrac{3a^2+3}{\left(a-3\right)\left(a+3\right)}\right)\cdot\dfrac{a-3}{a+1}\)
\(=\dfrac{2a\left(a-3\right)+a\left(a+3\right)-3a^2-3}{\left(a+3\right)\left(a-3\right)}\cdot\dfrac{a-3}{a+1}\)
\(=\dfrac{2a^2-6a+a^2+3a-3a^2-3}{\left(a+3\right)}\cdot\dfrac{1}{a+1}\)
\(=\dfrac{-3a-3}{\left(a+1\right)\left(a+3\right)}=\dfrac{-3}{a+3}\)
b: |a|=2
=>\(\left[{}\begin{matrix}a=2\left(nhận\right)\\a=-2\left(nhận\right)\end{matrix}\right.\)
Thay a=2 vào A, ta được:
\(A=\dfrac{-3}{2+3}=\dfrac{-3}{5}\)
Thay a=-2 vào A, ta được:
\(A=\dfrac{-3}{-2+3}=\dfrac{-3}{1}=-3\)
c: Để A nguyên thì \(-3⋮a+3\)
=>\(a+3\in\left\{1;-1;3;-3\right\}\)
=>\(a\in\left\{-2;-4;0;-6\right\}\)
Bài 13:
a: ĐKXĐ: \(x\notin\left\{2;-2;\dfrac{1}{2};0\right\}\)
\(B=\left(\dfrac{x+2}{2-x}-\dfrac{4x^2}{x^2-4}-\dfrac{2-x}{x+2}\right):\dfrac{2x^2-x}{x^2-2x}\)
\(=\left(\dfrac{-\left(x+2\right)}{x-2}-\dfrac{4x^2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{x+2}\right)\cdot\dfrac{x\left(x-2\right)}{x\left(2x-1\right)}\)
\(=\dfrac{-\left(x+2\right)^2-4x^2+\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x-2}{2x-1}\)
\(=\dfrac{-x^2-4x-4-4x^2+x^2-4x+4}{\left(x+2\right)}\cdot\dfrac{1}{2x-1}\)
\(=\dfrac{-4x^2-8x}{\left(x+2\right)\left(2x-1\right)}\)
\(=\dfrac{-4x\left(x+2\right)}{\left(x+2\right)\left(2x-1\right)}=\dfrac{-4x}{2x-1}\)
b: |x|=3
=>\(\left[{}\begin{matrix}x=3\left(nhận\right)\\x=-3\left(nhận\right)\end{matrix}\right.\)
Thay x=3 vào B, ta được:
\(B=\dfrac{-4\cdot3}{2\cdot3-1}=\dfrac{-12}{5}\)
Thay x=-3 vào B, ta được:
\(B=\dfrac{-4\cdot\left(-3\right)}{2\cdot\left(-3\right)-1}=\dfrac{12}{-7}=\dfrac{-12}{7}\)
c: Để B nguyên thì \(-4x⋮2x-1\)
=>\(-4x+2-2⋮2x-1\)
=>\(-2⋮2x-1\)
=>\(2x-1\in\left\{1;-1;2;-2\right\}\)
=>\(x\in\left\{0;1;\dfrac{3}{2};-\dfrac{1}{2}\right\}\)
mà x nguyên và \(x\notin\left\{2;-2;\dfrac{1}{2};0\right\}\)
nên x=1
làm bài 1 trước nha mn cảm ơn mn :D
