00:01
So in this problem, we're being asked to determine if the given statement is true or false.
00:05
So we have this equation, 1 divided by x minus 1 times x plus 2, and it's equal to 1 over x squared plus x minus 2.
00:12
And they're telling us that the solution would be all real numbers.
00:15
Well, remember, in order for it to be all real numbers, that would mean that the two equations are equal and no values of x will cause either of our denominators to be zero.
00:25
Well, in this case, let's see if the two fractions are in fact equal.
00:28
So if we multiply out our denominator on the left -hand side by using the foil method, we have x times x, which is x squared, x times 2 is positive 2x, negative 1 times x is negative x, and negative 1 times 2 is minus 2.
00:44
And if we combine our light terms, 2x minus x, so we would have 1 over x squared plus x minus 2...