Question

x+115/15+x+119/19 = x+217/117+x+327/227

Answer 1

\(\frac{x+115}{15}+\frac{x+119}{19}=\frac{x+217}{117}+\frac{x+327}{227}\)

\(\Leftrightarrow\left(\frac{x+115}{15}-1\right)+\left(\frac{x+119}{19}-1\right)=\left(\frac{x+217}{117}-1\right)+\left(\frac{x+327}{227}-1\right)\)

\(\Leftrightarrow\frac{x+100}{15}+\frac{x+100}{19}=\frac{x+100}{117}+\frac{x+100}{227}\)

\(\Leftrightarrow\frac{x+100}{15}+\frac{x+100}{19}-\frac{x+100}{117}-\frac{x+100}{227}=0\)

\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{15}+\frac{1}{19}-\frac{1}{117}-\frac{1}{227}\right)=0\)

\(\Leftrightarrow x+100=0\)

\(\Leftrightarrow x=-100\)