Option A: [tex]\frac{10}{9}[/tex] is the solution of x
Explanation:
The given expression is [tex]\frac{7}{(x+2)}+\frac{11}{(x-5)}=\frac{7}{(x+2)(x-5)}[/tex]
We need to determine the value of x.
The value of x can be determined by solving the expression for x.
Taking LCM , we get,
[tex]\frac{7(x-5)+11(x+2)}{(x+2)(x-5)}=\frac{7}{(x+2)(x-5)}[/tex]
Since, the denominator is common for both sides of the equation, let us cancel the denominator.
Thus, we have,
[tex]7(x-5)+11(x+2)=7[/tex]
Multiplying the terms within the bracket, we get,
[tex]7x-35+11x+22=7[/tex]
Adding the like terms, we get,
[tex]18x-13=7[/tex]
Adding both sides of the equation by 13, we have,
[tex]18x=20[/tex]
Dividing both sides of the equation by 18,
[tex]x=\frac{20}{18}[/tex]
Simplifying, we get,
[tex]x=\frac{10}{9}[/tex]
Thus, the solution is [tex]\frac{10}{9}[/tex]
Therefore, Option A is the correct answer.
