5A.
a)
$\frac{x-5}{2015}$ + $\frac{x-4}{2016}$ = $\frac{x-3}{2017}$ + $\frac{x-2}{2018}$
⇔ ( $\frac{x-5}{2015}$ - 1) + ($\frac{x-4}{2016}$ -1 ) = ($\frac{x-3}{2017}$ - 1) + ( $\frac{x-2}{2018}$ - 1 )
⇔ $\frac{x-2020}{2015}$ + $\frac{x-2020}{2016}$ = $\frac{x-2020}{2017}$ + $\frac{x-2020}{2018}$
⇔ $\frac{x-2020}{2015}$ + $\frac{x-2020}{2016}$ - $\frac{x-2020}{2017}$ - $\frac{x-2020}{2018}$ = 0
⇔ (x-2020) ( $\frac{1}{2015}$ + $\frac{1}{2016}$ - $\frac{1}{2017}$ - $\frac{1}{2018}$ ) = 0
⇔ x-2020 = 0
⇔ x = 2020
Vậy phương trình có tập nghiệm S ={2020}
b)
$\frac{x-1}{12}$ - $\frac{2x-12}{14}$ = $\frac{3x-14}{25}$ - $\frac{4x-29}{27}$
⇔ ( $\frac{x-1}{12}$ - 1) - ( $\frac{2x-12}{14}$ - 1) = ( $\frac{3x-14}{25}$ - 1 ) - ( $\frac{4x-29}{27}$ - 1 )
⇔ $\frac{x-13}{12}$ - $\frac{2x-26}{14}$ - $\frac{3x-39}{25}$ - $\frac{4x-52}{27}$ = 0
⇔ $\frac{x-13}{12}$ - $\frac{2(x-13)}{14}$ - $\frac{3(x-13)}{25}$ - $\frac{4(x-13)}{27}$ = 0
⇔ (x-13) ($\frac{1}{12}$ - $\frac{2}{14}$ - $\frac{3}{25}$ - $\frac{4}{27}$) = 0
⇔ x-13 = 0
⇔ x = 13
Vậy phương trình có tập nghiệm S = {13}
5B. Làm tương tự như trên nha bạn
