Question

How would I solve this Rational Equation?

Solve for all values of x.

Answer 1

9514 1404 393

Answer:

x = 4

Explanation:

I like to put these in the form f(x) = 0. We can do that by subtracting the right side. Common factors can be cancelled from numerator and denominator, provided they are not zero.

`(7)/(x+3)+(3)/(x-3)-(x)/(x-3)=0\\\\ (7(x-3)+(x+3)(3-x))/((x+3)(x-3))=0\\\\((x-3)(4-x))/((x-3)(x+3))=0\\\\ (4-x)/(x+3)=0\qquad x\\e3\\\\x=4 \qquad\text{equate the numerator to zero, add $x$}`

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If you leave the numerator as (x-3)(4-x), then there are two values of x that make it zero. Because x=3 makes the equation "undefined", it cannot be considered to be a solution.