Question 68304

To solve a Rational Equation:
1. Multiply each term of the equation by the least common denominator.
With the problem 5 + R = R + 5 so the Least common denominator is (R+5)(R+2)
{{{ ((R+5)(R+2))(3/(5+R)) + ((R+5)(R+2))(R/(R+2))=((R+5)(R+2))((R+4)/(R+5)) }}}
Solve the equation
{{{(3(R+2)) + (R(R+5))=(R+4)(R+2)}}} Distributive Property
{{{ (3R+6) + (R^2+5R) = (R^2 + 2R + 4R + 8)}}}
{{{ 3R + 6 + R^2 + 5R = R^2 + 6R + 8)}}}   
{{{ R^2 + 8R + 6 - R^2 - 6R - 8 = 0}}}     
{{{ 2R - 2 = 0}}}               Combine Like terms
{{{2R - 2 + 2 = 0 + 2}}}        Add both sides with 2
{{{ 2R/2 = 2/2}}}               divide both sides with 2
Answer is R = 1

Checking :
{{{(3/(5+R)) + (R/(R+2))=(R+4)/(R+5) }}} , R = 1
{{{(3/(5+1)) + (1/(1+2))=(1+4)/(1+5) }}}
{{{(3/6) + (1/3)= 5/6 }}}
{{{(3/6) + (2/6) = 5/6}}}
{{{ 5/6 = 5/6}}} True