Câu hỏi của Lyly Luta

Question

thực hiện phép tính

a) (x3+8y3):(2y+x) b.$\frac{a-1}{2\left(a-4\right)}+\frac{a}{a-4}$ c. (x3+3x2y+3xy2+y3):(2x+2y)

d. (x-5)2+(7-x)(x+2) e.$\frac{3x}{x-2}-\frac{2x+1}{2-x}$ f. \(\left(\frac{x+2}...

Nguyễn Nam · Accepted Answer

) $\dfrac{x^3+8y^3}{2y+x}$

$=\dfrac{x^3+\left(2y\right)^3}{x+2y}$

$=\dfrac{\left(x+2y\right)\left[x^2+x.2y+\left(2y\right)^2\right]}{x+2y}$

$=x^2+2xy+4y^2$

b) $\dfrac{a-1}{2\left(a-4\right)}+\dfrac{a}{a-4}$ MTC: $2\left(a-4\right)$

$=\dfrac{a-1}{2\left(a-4\right)}+\dfrac{2a}{2\left(a-4\right)}$

$=\dfrac{a-1+2a}{2\left(a-4\right)}$

$=\dfrac{3a-1}{2\left(a-4\right)}$

c) $\dfrac{x^3+3x^2y+3xy^2+y^3}{2x+2y}$

$=\dfrac{\left(x+y\right)^3}{2\left(x+y\right)}$

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

d) $\left(x-5\right)^2+\left(7-x\right)\left(x+2\right)$

$=\left(x^2-2.x.5+5^2\right)+\left(7x+14-x^2-2x\right)$

$=x^2-10x+25+7x+14-x^2-2x$

$=39-5x$

e) $\dfrac{3x}{x-2}-\dfrac{2x+1}{2-x}$

$=\dfrac{3x}{x-2}+\dfrac{2x+1}{x-2}$

$=\dfrac{3x+2x+1}{x-2}$

$=\dfrac{5x+1}{x-2}$

h) $\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{3x+6}{4-9x^2}$

$=\dfrac{1}{3x-2}-\dfrac{1}{3x+2}+\dfrac{3x+6}{9x^2-4}$

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

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

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

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

$=\dfrac{3x+10}{\left(3x-2\right)\left(3x+2\right)}$Câu trả lời: ) $\dfrac{x^3+8y^3}{2y+x}$