\(\frac{x+2}{13}+\frac{2x+45}{15}=\frac{3x+8}{37}+\frac{4x+69}{9}\)

\(\Leftrightarrow\left(\frac{x+2}{13}+1\right)+\left(\frac{2x+45}{15}-1\right)=\left(\frac{3x+8}{37}+1\right)+\left(\frac{4x+69}{9}-1\right)\)

\(\Leftrightarrow\frac{x+15}{13}+\frac{2\left(x+15\right)}{15}=\frac{3\left(x+15\right)}{37}+\frac{4\left(x+15\right)}{9}\)

\(\Leftrightarrow\left(x+15\right)\left(\frac{1}{13}+\frac{2}{15}-\frac{3}{7}-\frac{4}{9}\right)=0\)

mà \(\left(\frac{1}{13}+\frac{2}{15}-\frac{3}{7}-\frac{4}{9}\right)\ne0\)

\(\Leftrightarrow x+15=0\Leftrightarrow x=-15\)

Vậy x=-15

k cho mình nha

Giải phương trình

\(\dfrac{x+2}{13}+\dfrac{2x+45}{15}=\dfrac{3x+8}{37}+\dfrac{4x+69}{9}\)

\(\Leftrightarrow\)\(\dfrac{x+2}{13}+1+\dfrac{2x+45}{15}-1=\dfrac{3x+8}{37}+1+\dfrac{4x+69}{9}-1\)

\(\Leftrightarrow\)\(\dfrac{x+2}{13}+\dfrac{13}{13}+\dfrac{2x+45}{15}-\dfrac{15}{15}=\dfrac{3x+8}{37}+\dfrac{37}{37}+\dfrac{4x+69}{9}-\dfrac{9}{9}\)

\(\Leftrightarrow\dfrac{x+15}{13}+\dfrac{2x+30}{15}=\dfrac{3x+45}{37}+\dfrac{4x+60}{9}\)

\(\Leftrightarrow\dfrac{x+15}{13}+\dfrac{2\left(x+15\right)}{15}=\dfrac{3\left(x+15\right)}{37}+\dfrac{4\left(x+15\right)}{9}\)

\(\Leftrightarrow\left(x+15\right)\left(\dfrac{1}{13}+\dfrac{2}{15}\right)=\left(x+15\right)\left(\dfrac{3}{37}+\dfrac{4}{9}\right)\)

\(\Leftrightarrow\left(x+15\right)\left(\dfrac{1}{13}+\dfrac{2}{15}\right)-\left(x+15\right)\left(\dfrac{3}{37}+\dfrac{4}{9}\right)=0\)

\(\Leftrightarrow\left(x+15\right)\left(\dfrac{1}{13}+\dfrac{2}{15}-\dfrac{3}{37}-\dfrac{4}{9}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+15=0\\\dfrac{1}{13}+\dfrac{2}{15}-\dfrac{3}{37}-\dfrac{4}{9}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-15\\\dfrac{1}{13}+\dfrac{2}{15}-\dfrac{3}{37}-\dfrac{4}{9}\ne0\end{matrix}\right.\)

Do đó: \(x=-15\)

Vậy \(S=\left\{-15\right\}\)

bạn cộng 2 vế hoặc trừ đi 1 số nào đó là ra

\(\dfrac{x+2}{13}+\dfrac{2x+45}{15}=\dfrac{3x+8}{37}+\dfrac{4x+69}{9}\)

\(\Leftrightarrow\dfrac{x+2}{13}+1+\dfrac{2x+45}{15}-1=\dfrac{3x+8}{37}+1+\dfrac{4x+69}{9}-1\)\(\Leftrightarrow\dfrac{x+15}{13}+\dfrac{2\left(x+15\right)}{15}=\dfrac{3\left(x+15\right)}{37}+\dfrac{4\left(x+15\right)}{9}\)\(\Leftrightarrow\dfrac{x+15}{13}+\dfrac{2\left(x+15\right)}{15}-\dfrac{3\left(x+15\right)}{37}-\dfrac{4\left(x+15\right)}{9}=0\)\(\Leftrightarrow\left(x+15\right)\left(\dfrac{1}{13}+\dfrac{2}{15}-\dfrac{3}{37}+\dfrac{4}{9}\right)=0\)

\(\Leftrightarrow x+15=0\)

\(\Leftrightarrow x=-15\)

Vậy x = -15.

\(\dfrac{x+2}{13}+\dfrac{2x+45}{15}=\dfrac{3x+8}{37}+\dfrac{4x+69}{9}\\ \Leftrightarrow\dfrac{x+2}{13}+1+\dfrac{2x+45}{15}-1=\dfrac{3x+8}{37}+1+\dfrac{4x+69}{9}-1\\ \Leftrightarrow\dfrac{x+15}{13}+\dfrac{2x+30}{15}=\dfrac{3x+45}{37}+\dfrac{4x+60}{9}\)

\(\Leftrightarrow\left(x+15\right)\dfrac{1}{13}+\left(x+15\right)\dfrac{2}{15}=\left(x+15\right)\dfrac{3}{37}+\left(x+15\right)\dfrac{4}{9}\\ \Leftrightarrow\left(x+15\right)\left(\dfrac{1}{13}+\dfrac{2}{15}-\dfrac{3}{37}-\dfrac{4}{9}\right)=0\)

vì:\(\dfrac{1}{13}+\dfrac{2}{15}-\dfrac{3}{37}-\dfrac{4}{9}\ne0\) nên:

x+15=0 =>x=-15

vậy phương trình có tập nghiệm là S={-15}

<=>(x+2/13)+1+(2x+45/15)-1 = (3x+8/37)+1+(4x+69/9)-1

<=> x+15/13 + 2x+30/15 = 3x+45/37 + 4x+60/9

<=>(x+15)(1/13+2/15-3/37-4/9) = 0

<=> x+15=0( vì 1/13+2/15-3/37-4/9=0)

<=>x=-15......

a)x+1/15 + x+2/7 + x+4/4 + 6 = 0    

\(\Rightarrow\left(\frac{x+1}{15}+1\right)+\left(\frac{x+2}{7}+2\right)+\left(\frac{x+4}{4}+3\right)+\left(\frac{x+16}{\frac{1}{6}\left(x+16\right)}\right)=0\)\(\Rightarrow\frac{x+16}{15}+\frac{x+16}{7}+\frac{x+16}{4}+\frac{x+16}{\frac{1}{6}\left(x+16\right)}=0\)

\(\Rightarrow\left(x+16\right)\left(\frac{1}{15}+\frac{1}{7}+\frac{1}{4}+\frac{1}{\frac{1}{6}\left(x+16\right)}\right)=0\)

\(\Rightarrow x+16=0\).Do \(\frac{1}{15}+\frac{1}{7}+\frac{1}{4}+\frac{1}{\frac{1}{6}\left(x+16\right)}\ne0\)

\(\Rightarrow x=-16\)

b)tương tự