Question 1209876
<br>
{{{(2x+5)/(x+3)=12/(x-1)}}}<br>
{{{(2x+5)/(x+3)-12/(x-1)=0}}}<br>
Multiply everything by (x+3)(x-1) to clear fractions.
{{{(2x+5)(x-1)-12(x+3)=0}}}
{{{2x^2+3x-5-12x-36=0}}}
{{{2x^2-9x-41=0}}}<br>
That doesn't factor, so use the quadratic formula.<br>
{{{x=(9+sqrt(81+328))/4=(9+sqrt(409))/4}}} and {{{x=(9-sqrt(81+328))/4=(9-sqrt(409))/4}}}<br>
To several decimal places, the x values where the two graphs intersect are -2.806 and 7.306<br>
The problem asks for the {{{cross(largest)}}} larger of the two values.<br>
ANSWER: {{{(9+sqrt(409))/4}}}, or approximately 7.306<br>