Toán Lớp 8: x/2x-3 + x/2x+2 =2x/(x+1)(x-3) -

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Toán Lớp 8: x/2x-3 + x/2x+2 =2x/(x+1)(x-3)

Nhiên Tháng Mười 27, 2022 Toán học 1 Comment 0 views

Toán Lớp 8: x/2x-3 + x/2x+2 =2x/(x+1)(x-3)

Comments ( 1 )

giahan44
27 Tháng Mười, 2022 at 12:24 chiều

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ĐK:{(xne3/2),(xne-1),(xne3):}

x/(2x-3)+x/(2x+2)=(2x)/((x+1)(x-3))

->x/(2x-3)+x/(2x+2)-(2x)/((x+1)(x-3))=0

->x(1/(2x-3)+1/(2x+2)-2/((x+1)(x-3)))=0

Ta có : 1/(2x-3)+1/(2x+2)-2/((x+1)(x-3))

=(2x+2)(x+1)(x-3)+(2x-3)(x+1)(x-3)-2(2x-3)(2x+2)

=(2x+2)(x^2-2x-3)+(2x-3)(x^2-2x-3)-2(4x^2-2x-6)

=2x^3-2x^2-10x-6+2x^3-7x^2+9-8x^2+4x+12

=4x^3-17x^2-6x+15

->\(\left[ \begin{array}{l}x=0\\4x^3-17x^2-6x+15=0\end{array} \right.\)

->\(\left[ \begin{array}{l}x=0\\(x+1)=0\\(4x^2-21x+15)=0\end{array} \right.\)

->\(\left[ \begin{array}{l}x=0\\x=-1(KTM)\\x=\frac{21-\sqrt{201}}{8}\\x=\frac{21+\sqrt{201}}{8}\end{array} \right.\)

Vậy S={0;(21+-\sqrt{201})/8}

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