WEBVTT

1
00:00:00.000 --> 00:00:06.316
Here is the problem: x/(x plus 9) plus 1/(x minus 7) equals 1.

2
00:00:06.766 --> 00:00:11.456
A linear equation in x: isolate x using inverse operations.

3
00:00:12.256 --> 00:00:13.730
Start with the equation.

4
00:00:14.180 --> 00:00:30.562
Multiply both sides by x ^ 2 +2 cdot x minus 63 to clear the fractions. This is only valid where x ^ 2 plus 2 times x minus 63 not equal to 0, so any value that makes it zero is excluded at the end.

5
00:00:31.012 --> 00:00:32.138
Isolate x.

6
00:00:32.938 --> 00:00:36.665
Now look at the graph of the left side minus the right side.

7
00:00:37.115 --> 00:00:40.842
It crosses zero exactly at the solutions we found.

8
00:00:41.642 --> 00:00:43.883
So the answer is x equals 9.

9
00:00:44.333 --> 00:00:53.482
Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

10
00:00:54.282 --> 00:01:00.679
x equals 9: left side equals 1, right side equals 1, which checks out.