Question

Solve the rational equation, State the excluded values in the picture below

Answer 1

`\begin{gathered} (x+7)/(x+4)-1=(x+10)/(2(x+4)) \\ (x+7-(x+4))/(x+4)=(x+10)/(2(x+4)) \\ (x+7-x-4)/(x+4)=(x+10)/(2(x+4)) \\ (3)/(x+4)=(x+10)/(2(x+4)) \\ \text{cross multiply} \\ 3*2*(x+4)=(x+4)(x+10) \\ 6(x+4)=(x+4)(x+10) \\ \text{divide both sides by (x+4)} \\ 6=x+10 \\ x=6-10 \\ x=-4 \end{gathered}`

The excluded value is x = - 4. The excluded value is the number that will make the denominator of the fraction equals to zero.