Question

giải phương trình:

a) (x+3)² - (x-3)² = 6x+18

b) \(\frac{x+3}{x-2}\) = \(\frac{5}{\left(x-2\right)\left(3-x\right)}\)

c) \(\frac{12x^2+30x-21}{16x^2-9}\) - \(\frac{3x-7}{3x-4}\) = \(\frac{6x+5}{4x+3}\)

d) \(\frac{4}{x+1}\) - \(\frac{2}{x-2}\) = \(\frac{x+3}{x^2-x-2}\)

giúp mình với! cần gấp!

Answer 1

Lời giải:

a) $(x+3)^2-(x-3)^2=6x+18$

$\Leftrightarrow 12x=6x+18\Leftrightarrow 6x=18\Rightarrow x=3$

b) ĐK:$x\neq 2; x\neq 3$

PT $\Rightarrow x+3=\frac{5}{3-x}$

$\Rightarrow (x+3)(3-x)=5$

$\Rightarrow 9-x^2=5$

$\Rightarrow x^2=4\Rightarrow x=\pm 2$. Kết hợp với ĐKXĐ suy ra $x=-2$

c) ĐKXĐ: $x\neq \frac{\pm 3}{4}$

PT $\Leftrightarrow \frac{12x^2+30x-21}{(4x-3)(4x+3)}-\frac{(3x-7)(3x+4)}{(4x-3)(4x+3)}=\frac{(6x+5)(4x-3)}{(4x-3)(4x+3)}$

$\Rightarrow 12x^2+30x-21-(3x-7)(4x+3)=(6x+5)(4x-3)$

$\Leftrightarrow -24x^2+47x+15=0$

$\Rightarrow x=\frac{47\pm \sqrt{3649}}{48}$

d)

ĐK: $x\neq -1; x\neq 2$

PT $\Leftrightarrow \frac{4(x-2)}{(x+1)(x-2)}-\frac{2(x+1)}{(x-2)(x+1)}=\frac{x+3}{(x+1)(x-2)}$

$\Rightarrow 4(x-2)-2(x+1)=x+3$
$\Rightarrow x=13$ (t.m)