Thực hiện phép tính:
`a, 1/(3x-2)-4/(3x+2)-(-10x+8)/(9x^2-4)`
`b,3/(2x^2+2x)+(2x-1)/(x^2-1)-2/x`
`c, (3x)/(5x+5y)-x/(10x-10y)`
Thực hiện phép tính:
`a, 1/(3x-2)-4/(3x+2)-(-10x+8)/(9x^2-4)`
`b,3/(2x^2+2x)+(2x-1)/(x^2-1)-2/x`
`c, (3x)/(5x+5y)-x/(10x-10y)`
Đáp án:
a) \(\dfrac{{x + 2}}{{\left( {3x – 2} \right)\left( {3x + 2} \right)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{3x + 2 – 4\left( {3x – 2} \right) + 10x – 8}}{{\left( {3x – 2} \right)\left( {3x + 2} \right)}}\\
= \dfrac{{13x – 6 – 12x + 8}}{{\left( {3x – 2} \right)\left( {3x + 2} \right)}}\\
= \dfrac{{x + 2}}{{\left( {3x – 2} \right)\left( {3x + 2} \right)}}\\
b)\dfrac{3}{{2x\left( {x + 1} \right)}} + \dfrac{{2x – 1}}{{\left( {x – 1} \right)\left( {x + 1} \right)}} – \dfrac{2}{x}\\
= \dfrac{{3\left( {x – 1} \right) + 2x\left( {2x – 1} \right) – 4\left( {{x^2} – 1} \right)}}{{2x\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{3x – 3 + 4{x^2} – 2x – 4{x^2} + 4}}{{2x\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{x + 1}}{{2x\left( {x – 1} \right)\left( {x + 1} \right)}} = \dfrac{1}{{2x\left( {x – 1} \right)}}\\
c)\dfrac{{3x}}{{5\left( {x + y} \right)}} – \dfrac{x}{{10\left( {x – y} \right)}}\\
= \dfrac{{6x\left( {x – y} \right) – x\left( {x + y} \right)}}{{10\left( {x – y} \right)\left( {x + y} \right)}}\\
= \dfrac{{6{x^2} – 6xy – {x^2} – xy}}{{10\left( {x – y} \right)\left( {x + y} \right)}}\\
= \dfrac{{5{x^2} – 7xy}}{{10\left( {x – y} \right)\left( {x + y} \right)}}
\end{array}\)