Question

Help!

5x/x+1=4x/x-1+10/x^2-1

Answer 1

\[\frac{5x}{x+1}=\frac{4x}{x-1}+\frac{10}{x^2-1}\]
\[\frac{5x}{x+1}=\frac{4x}{x-1}+\frac{10}{(x-1)(x+1)}\]
\[(x-1)(x+1)(\frac{5x}{x+1})=(x-1)(x+1)(\frac{4x}{x-1})+(x-1)(x+1)(\frac{10}{(x-1)(x+1)})\]
\[\frac{5x(x-1)}{(x-1)(x+1)}=\frac{4x(x+1)}{(x-1)(x+1)}+\frac{10}{(x-1)(x+1)}\]
\[5x(x-1)=4x(x+1)+10\]
\[5x^2-5x=4x^2+4x+10\]
\[x^2-9x-10=0\]
\[(x-10)(x+1)=0\]
\[x=10, -1\]
Because -1 is not in the domain of this rational equation, x=10 is your only solution

Answer 2

Thank you so much!

Answer 3

yw