### Video Transcript

Given that π sub one of π₯ is equal to seven plus π over π₯ minus seven, π sub two of π₯ is equal to two over π₯ minus seven, and π sub one of π₯ is equal to π sub two of π₯, what is the value of π?

Here, we have two rational functions. And weβre told that the two functions are equal to each other. So that means that for π sub one of π₯ to be called π sub two of π₯, the functions are equal for all values of π₯, not just for a certain value or values. So we can say that seven plus π over π₯ minus seven equals two over π₯ minus seven. Now, look really carefully. The denominator of each of our functions is equal. And so for the function π sub one of π₯ to be equal to the function π sub two of π₯, their numerator must also be equal. So seven plus π must be equal to two.

Now, we have this; we can solve this equation for π fairly easily. Weβre going to subtract seven from both sides. And seven plus π minus seven is π. And two minus seven is negative five. And so we found the value of π; itβs negative five. Now, of course, we can check that what weβve done is correct by substituting π into our expression for the function π sub one of π₯. We get seven plus negative five over π₯ minus seven, which is two over π₯ minus seven as required.