Question

giải các pt sau:

a) 5-(x-6)=4(3-2x)

b) 2x(x-3)+5(x-3)=0

c)\(\frac{3x-5}{x-2}\)-\(\frac{2x-5}{x-1}\)=1

Answer 1

a) 5 - (x - 6) = 4(3 - 2x)

<=> 5 - x + 6 = 12 - 8x

<=> -x + 8x = 12 - 11

<=> 7x = 1

<=> x = 1/7

Vậy S = {1/7}

b) 2x(x - 3) + 5(x - 3) = 0

<=> (2x + 5)(x - 3) = 0

<=> \(\orbr{\begin{cases}2x+5=0\\x-3=0\end{cases}}\)

<=> \(\orbr{\begin{cases}x=-\frac{5}{2}\\x=3\end{cases}}\)

Vậy S = {-5/2; 3}

c)ĐK: x \(\ne\)1; x \(\ne\)2

 \(\frac{3x-5}{x-2}-\frac{2x-5}{x-1}=1\)

<=> \(\frac{\left(3x-5\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}-\frac{\left(2x-5\right)\left(x-2\right)}{\left(x-1\right)\left(x-2\right)}=\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}\)

<=> 3x² - 8x + 5 - 2x² + 9x - 10 = x² - 3x + 2

<=> x² + x - 5 = x² - 3x + 2

<=> x² + x  - x² + 3x = 2 + 5

<=> 4x = 7

<=> x = 7/4 

Vậy S = {7/4}