Toán Lớp 8: b1 thực hiện phép tính
a,5x-1/3x^2y + x+1/3x^2y
b, 7/12xy^2 + 11/ 18x^3y
c, x/x+2+7x-16/(x+2)(4x-7)
d, 3x/x^2-y^2-x^2/y^2-x
e, 2x^2-15/x^2-6x+9+15-6x/x^2-6x+9
f, x+1/2x-2-2x/x^2-1
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Toán Lớp 8: b1 thực hiện phép tính
a,5x-1/3x^2y + x+1/3x^2y
b, 7/12xy^2 + 11/ 18x^3y
c, x/x+2+7x-16/(x+2)(4x-7)
d, 3x/x^2-y^2-x^2/y^2-x
e, 2x^2-15/x^2-6x+9+15-6x/x^2-6x+9
f, x+1/2x-2-2x/x^2-1
Comments ( 1 )
a)\dfrac{{5x – 1}}{{3{x^2}y}} + \dfrac{{x + 1}}{{3{x^2}y}} = \dfrac{{5x – 1 + x + 1}}{{3{x^2}y}}\\
= \dfrac{{6x}}{{3{x^2}y}} = \dfrac{2}{{xy}}\\
b)\dfrac{7}{{12x{y^2}}} + \dfrac{{11}}{{18{x^3}y}}\\
= \dfrac{{7.3{x^2} + 11.2y}}{{36{x^3}{y^2}}}\\
= \dfrac{{21{x^2} + 22y}}{{36{x^3}{y^2}}}\\
c)\dfrac{x}{{x + 2}} + \dfrac{{7x – 16}}{{\left( {x + 2} \right)\left( {4x – 7} \right)}}\\
= \dfrac{{x\left( {4x – 7} \right) + 7x – 16}}{{\left( {x + 2} \right)\left( {4x – 7} \right)}}\\
= \dfrac{{4{x^2} – 7x + 7x – 16}}{{\left( {x + 2} \right)\left( {4x – 7} \right)}}\\
= \dfrac{{4\left( {{x^2} – 4} \right)}}{{\left( {x + 2} \right)\left( {4x – 7} \right)}}\\
= \dfrac{{4\left( {x – 2} \right)}}{{4x – 7}}\\
= \dfrac{{4x – 8}}{{4x – 7}}\\
d)\dfrac{{3x}}{{{x^2} – {y^2}}} – \dfrac{{{x^2}}}{{{y^2} – {x^2}}}\\
= \dfrac{{3x + {x^2}}}{{{x^2} – {y^2}}}\\
e)\dfrac{{2{x^2} – 15}}{{{x^2} – 6x + 9}} + \dfrac{{15 – 6x}}{{{x^2} – 6x + 9}}\\
= \dfrac{{2{x^2} – 6x}}{{{{\left( {x – 3} \right)}^2}}}\\
= \dfrac{{2x\left( {x – 3} \right)}}{{{{\left( {x – 3} \right)}^2}}}\\
= \dfrac{{2x}}{{x – 3}}\\
e)\dfrac{{x + 1}}{{2x – 2}} – \dfrac{{2x}}{{{x^2} – 1}}\\
= \dfrac{{{{\left( {x + 1} \right)}^2} – 2x.2}}{{2\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{{x^2} – 2x + 1}}{{2\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{{{\left( {x – 1} \right)}^2}}}{{2\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{x – 1}}{{2\left( {x + 1} \right)}}
\end{array}$