Question

bài 1: thực hiện phép tính

a, x+1/2x+6 + 2x

b, 3/2x+6 - x-6/2x^2+6x
c, x/x-2y + x/x+2y + 4xy/4y^2-x^2
d, 1/3x-2 - 1/3x+2 - 3x-6/4-9x^2

Answer 1

\(a.\dfrac{x+1}{2x+6}+2x=\dfrac{x+1+4x^2+12x}{2x+6}=\dfrac{4x^2+13x+1}{2x+6}\) ( x # -3)

\(b.\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\) ( x # - 3)

Các câu còn lại tương tự .

Answer 2

\(a,\dfrac{x+1}{2x+6}+2x\)

\(=\dfrac{x+1}{2x+6}+\dfrac{2x\left(2x+6\right)}{2x+6}\)

\(=\dfrac{x+1+4x^2+12x}{2x+6}\)

\(=\dfrac{4x^2+13x+1}{2x+6}\)

\(b,\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)

\(=\dfrac{3x}{2x^2+6x}-\dfrac{x-6}{2x^2-6x}\)

\(=\dfrac{2x-6}{2x^2+6x}=\dfrac{2\left(x-3\right)}{2x\left(x+3\right)}=\dfrac{x-3}{x^2+3x}\)

\(c,\dfrac{x}{x-2y}+\dfrac{x}{x+2y}+\dfrac{4xy}{4y^2-x^2}\)

\(=\dfrac{x\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)}+\dfrac{x\left(x-2y\right)}{\left(x+2y\right)\left(x-2y\right)}-\dfrac{4xy}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{2x^2-4xy}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\dfrac{2x\left(x-2y\right)}{\left(x-2y\right)\left(x+2y\right)}=\dfrac{2x}{x+2y}\)

\(d,\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{3x-6}{4-9x^2}\)

\(=\dfrac{3x+2}{\left(3x+2\right)\left(3x-2\right)}-\dfrac{3x-2}{\left(3x+2\right)\left(3x-2\right)}+\dfrac{3x-6}{\left(3x-2\right)\left(3x+2\right)}\)

\(=\dfrac{3x+2-3x+2+3x-6}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{3x-2}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{1}{3x+2}\)