giúp mk với rút gọn B=(1)/(2√x -1)-(2x+√x-3)/(1-4x) 14/07/2021 Bởi Quinn giúp mk với rút gọn B=(1)/(2√x -1)-(2x+√x-3)/(1-4x)
`B=1/(2\sqrt{x}-1)-(2x+\sqrt{x}-3)/(1-4x)` (ĐKXĐ: `x>=0; x \ne 1/4`) `B=(2\sqrt{x}+1+2x+\sqrt{x}-3)/((2\sqrt{x}-1)(2\sqrt{x}+1))` `B=(2x+3\sqrt{x}-2)/((2\sqrt{x}-1)(2\sqrt{x}+1))` `B=(2x-\sqrt{x}+4\sqrt{x}-2)/((2\sqrt{x}-1)(2\sqrt{x}+1))` `B=((2\sqrt{x}-1)(\sqrt{x}+2))/((2\sqrt{x}-1)(2\sqrt{x}+1))` `B=(\sqrt{x}+2)/(2\sqrt{x}+1)` Bình luận
Đáp án: $B=\dfrac{\sqrt{x}+2}{2\sqrt{x}+1}$ Giải thích các bước giải: ĐKXĐ: $x\ge 0;\,x\ne \dfrac{1}{4}$ $B=\dfrac{1}{2\sqrt{x}-1}-\dfrac{2x+\sqrt{x}-3}{1-4x}$ $=\dfrac{2\sqrt{x}+1}{(2\sqrt{x}-1)(2\sqrt{x}+1)}+\dfrac{2x+\sqrt{x}-3}{4x-1}$ $=\dfrac{2\sqrt{x}+1+2x+\sqrt{x}-3}{4x-1}$ $=\dfrac{2x+3\sqrt{x}-2}{4x-1}$ $=\dfrac{(2\sqrt{x}-1)(\sqrt{x}+2)}{(2\sqrt{x}-1)(2\sqrt{x}+1)}$ $=\dfrac{\sqrt{x}+2}{2\sqrt{x}+1}$. Bình luận
`B=1/(2\sqrt{x}-1)-(2x+\sqrt{x}-3)/(1-4x)` (ĐKXĐ: `x>=0; x \ne 1/4`)
`B=(2\sqrt{x}+1+2x+\sqrt{x}-3)/((2\sqrt{x}-1)(2\sqrt{x}+1))`
`B=(2x+3\sqrt{x}-2)/((2\sqrt{x}-1)(2\sqrt{x}+1))`
`B=(2x-\sqrt{x}+4\sqrt{x}-2)/((2\sqrt{x}-1)(2\sqrt{x}+1))`
`B=((2\sqrt{x}-1)(\sqrt{x}+2))/((2\sqrt{x}-1)(2\sqrt{x}+1))`
`B=(\sqrt{x}+2)/(2\sqrt{x}+1)`
Đáp án:
$B=\dfrac{\sqrt{x}+2}{2\sqrt{x}+1}$
Giải thích các bước giải:
ĐKXĐ: $x\ge 0;\,x\ne \dfrac{1}{4}$
$B=\dfrac{1}{2\sqrt{x}-1}-\dfrac{2x+\sqrt{x}-3}{1-4x}$
$=\dfrac{2\sqrt{x}+1}{(2\sqrt{x}-1)(2\sqrt{x}+1)}+\dfrac{2x+\sqrt{x}-3}{4x-1}$
$=\dfrac{2\sqrt{x}+1+2x+\sqrt{x}-3}{4x-1}$
$=\dfrac{2x+3\sqrt{x}-2}{4x-1}$
$=\dfrac{(2\sqrt{x}-1)(\sqrt{x}+2)}{(2\sqrt{x}-1)(2\sqrt{x}+1)}$
$=\dfrac{\sqrt{x}+2}{2\sqrt{x}+1}$.