I don't understand your notation for the first one. If , then if and only if . On the other hand, is not defined (division by zero). So, I don't understand what your answer: 7 means. Or, if f is a constant and the equals sign should be a plus sign (the equals sign and the plus sign share a key), then , then your answer should include an f.

For number 2, you should simplify the numerator first: . So, . For the denominator, you have . Then, you can cancel the from the numerator and denominator to get .

The third one:

We use the rational roots theorem to find factors of the numerator and denominator. For any polynomial, we only need to look at the coefficients of the highest power of x and of the lowest power of x to find rational roots. Possible roots of the numerator are . Possible roots of the denominator are . The ones that overlap are and . So, let's try all four and see which one works. Plug in values for . If is a factor of a polynomial, then plugging in will cause the polynomial to equal zero. Let's check:

, so is not a factor of the numerator.

, so is not a factor of the numerator.

, so is not a factor of the numerator.

, so is a factor of the numerator. Now let's check if it is a factor of the denominator.

, so is also a factor of the denominator.

The numerator becomes . This tells us that , so . So, the numerator is .

The denominator becomes . Equating coefficients, we have , , so , and , so . So, the denominator is . Cancelling, we get:

Now, you notice you can factor a 2 from both the numerator and denominator to get: