Chapter 9.6, Problem 5MRE

To determine

To find:the solution of the given equation by simplifying the equation.

Answer to Problem 5MRE

The equation can rewrite as: $\frac{\text{1}}{\text{2-x}}$ .

Explanation of Solution

Given:

  $\frac{\text{4}}{\text{x-2}}\text{+}\frac{\text{5}}{\text{2-x}}$ .

Concept used:

In the elimination method:

Either add or subtract equation to get an equation in one variable.

When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.

Calculation:

According to the given equation:

  $\frac{\text{4}}{\text{x-2}}\text{+}\frac{\text{5}}{\text{2-x}}$ .

Factor out $\text{-1}$ in the denominator of the second fraction and then rewrite the sum as difference.

  $\frac{\text{4}}{\text{x-2}}\text{+}\frac{\text{5}}{\text{2-x}}=\frac{\text{4}}{\text{x-2}}\text{+}\frac{\text{5}}{-\left(\text{x}-2\right)}=\frac{\text{4}}{\text{x-2}}-\frac{\text{5}}{\left(\text{x}-2\right)}$ .

Subtracting the equation having same L.C.M and distributing the negative in the denominator

  $\frac{\text{1}}{\text{-}\left(\text{x-2}\right)}\text{=}\frac{\text{1}}{\text{2-x}}$ .

Hence the equation can rewrite as: $\frac{\text{1}}{\text{2-x}}$ .