Question

tìm x biết

\(\frac{x+4}{2014}\)+\(\frac{x+3}{2015}\)=\(\frac{x+8}{2010}\)+\(\frac{x+7}{2011}\)

Answer 1

Ta có : 

\(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+8}{2010}+\frac{x+7}{2011}\)

\(\Leftrightarrow\)\(\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+8}{2010}+1\right)+\left(\frac{x+7}{2011}+1\right)\)

\(\Leftrightarrow\)\(\frac{x+4+2014}{2014}+\frac{x+3+2015}{2015}=\frac{x+8+2010}{2010}+\frac{x+7+2011}{2011}\)

\(\Leftrightarrow\)\(\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2010}+\frac{x+2018}{2011}\)

\(\Leftrightarrow\)\(\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2010}-\frac{x+2018}{2011}=0\)

\(\Leftrightarrow\)\(\left(x-2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)

Vì \(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\ne0\)

Nên \(x-2018=0\)

\(\Leftrightarrow\)\(x=2018\)

Vậy \(x=2018\)

Chúc bạn học tốt ~ 

Answer 2

Ta có: \(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+7}{2011}+\frac{x+8}{2010}\)

\(\Rightarrow\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+7}{2011}+1\right)+\left(\frac{x+8}{2010}+1\right)\)

\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2013}=\frac{x+2018}{2011}+\frac{x+2018}{2010}\)

\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2013}-\frac{x+2018}{2011}-\frac{x+2018}{2010}=0\)

\(\Rightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)

\(\Rightarrow x+2018=0\Rightarrow x=-2018\)

Chúc bn hc tốt! ^_^

Answer 3

\(\Leftrightarrow\frac{x+4}{2014}+1+\frac{x+3}{2015}+1=\frac{x+8}{2010}+1+\frac{x+7}{2011}+1\)
\(\Leftrightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2010}+\frac{x+2018}{2011}\)
\(\Leftrightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)
Do \(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\ne0\Rightarrow x+2018=0\Leftrightarrow x=-2018\)
 

Answer 4

uầy Lại nhầm nữa =.=" 

Sửa lại thành \(x+2018=0\)\(\Leftrightarrow\)\(x=-2018\) nhé bạn 

Answer 5

Ta có: \(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+8}{2010}+\frac{x+7}{2011}\) \(\Leftrightarrow\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+8}{2010}+1\right)+\left(\frac{x+7}{2011}+1\right)\)

\(\Leftrightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2010}+\frac{x+2018}{2011}\)

\(\Leftrightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2010}-\frac{x+2018}{2011}=0\)

\(\Leftrightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)

Vì \(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\ne0\) nên \(x+2018=0\Leftrightarrow x=-2018\)

Vậy...

Answer 6

\(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+8}{2010}+\frac{x+7}{2011}\)

\(\Leftrightarrow\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\)\(\left(\frac{x+8}{2010}+1\right)+\left(\frac{x+7}{2011}+1\right)\)( cộng cả hai vế với 2 )

\(\Leftrightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2010}+\frac{x+2018}{2011}\)

\(\Leftrightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2010}-\frac{x+2018}{2011}=0\)

\(\Leftrightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)

Mà  \(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\ne0\)

\(\Rightarrow x+2018=0\)

\(\Leftrightarrow x=-2018\)

Vậy  \(x=-2018\)