a: \(=\left(\dfrac{2x-3}{\left(2x-5\right)\left(2x-1\right)}-\dfrac{2x-8}{\left(2x-5\right)\left(x-4\right)}-\dfrac{3}{2x-1}\right)\cdot\dfrac{4x^2+4x-3}{-8x^2+2x+21}+1\)
\(=\dfrac{2x-3-2\left(2x-1\right)-3\left(x-4\right)}{\left(2x-1\right)\left(2x-5\right)}\cdot\dfrac{\left(2x+3\right)\left(2x-1\right)}{\left(4x-7\right)\cdot\left(-2x-3\right)}+1\)
\(=\dfrac{2x-3-4x+2-3x+12}{1}\cdot\dfrac{-1}{4x-7}+1\)
\(=\dfrac{5x-11}{4x-7}+1=\dfrac{9x-4}{4x-7}\)
b: |x|=1/2
=>x=1/2(loại) hoặc x=-1/2(nhận)
Khi x=-1/2 thì \(P=\dfrac{\dfrac{-9}{2}-4}{-2-7}=-\dfrac{17}{2}:\left(-9\right)=\dfrac{17}{18}\)
c: Để P là số nguyên thì \(36x-16⋮4x-7\)
\(\Leftrightarrow4x-7\in\left\{1;-1;47;-47\right\}\)
hay \(x\in\left\{2;\dfrac{3}{2};\dfrac{27}{2};-10\right\}\)
