Solve the equation: 5/(y - 4) = 3y/(y + 2) –

Tyra 2021-08-08 Answered
Solve the equation:
\(\displaystyle\frac{{5}}{{{y}-{4}}}={3}\frac{{y}}{{{y}+{2}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{y}^{{2}}–{2}{y}–{8}}}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Lacey-May Snyder
Answered 2021-08-09 Author has 25557 answers
\(\displaystyle\frac{{5}}{{{y}-{4}}}={3}\frac{{y}}{{{y}+{2}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{y}^{{2}}–{2}{y}–{8}}}\)
\(\displaystyle\frac{{5}}{{{y}-{4}}}={3}\frac{{y}}{{{y}+{2}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{\left({y}–{4}\right)}{\left({y}–{2}\right)}}}\)
\(\displaystyle\frac{{{5}{\left({y}+{2}\right)}}}{{{\left({y}-{4}\right)}{\left({y}+{2}\right)}}}=\frac{{{3}{y}{\left({y}–{4}\right)}}}{{{\left({y}+{2}\right)}{\left({y}-{4}\right)}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{\left({y}–{4}\right)}{\left({y}–{2}\right)}}}\)
\(\displaystyle{5}{y}+{10}={3}{y}^{{2}}–{12}{y}–{2}{y}^{{2}}+{14}{y}\)
\(\displaystyle-{y}^{{2}}+{3}{y}+{10}={0}\)
\(\displaystyle{y}^{{2}}–{3}{y}–{10}={0}\)
\(\displaystyle{\left({y}–{5}\right)}{\left({y}+{2}\right)}={0}\)
\(\displaystyle{y}={5}{\quad\text{or}\quad}{y}=-{2}\)
Not exactly what you’re looking for?
Ask My Question
22
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...