Question

4. (10 pts) Use the sweetheart method (Cross multiplication method) to solve(Show yourwork):X4x-4x-4(5 pts) Explain why your result is not valid.

Answer 1

EXPLANATION :

From the problem, we have :

`(x)/(x-4)=(4)/(x-4)`

Using cross multiplication :

`\begin{gathered} x(x-4)=4(x-4) \\ x^2-4x=4x-16 \\ x^2-4x-4x+16=0 \\ x^2-8x+16=0 \\ \text{ Factor completely :} \\ (x-4)(x-4)=0 \\ \text{ Equate factors to 0} \\ x-4=0 \\ x=4 \end{gathered}`

The value of x is 4

But this value of x will make the expression or equation undefined.

Because the denominator will become 0.

`\begin{gathered} (x)/(x-4)=(4)/(x-4) \\ \\ (4)/(4-4)=(4)/(4-4) \\ \\ (4)/(0)=(4)/(0) \end{gathered}`

Therefore, the result of x = 4 is NOT valid.