Question

Inverse Relations and Functions
What are some ways to solve rational equations?

Answer 1

You could eliminate the fractions through simplification or cross multiplication and then solve.

Answer 2

\[y=\frac{ax+b}{cx+d} \\ \text{ cross multiplication as suggested by Ark } \\ y(cx+d)=ax+b \\ \text{ distribute on left }\\ ycx+yd=ax+b \\ \text{ gather your terms with x on one side and all others go on opp side } \\ ycx-ax=b-yd \\ \text{ factor the x out on the left } \\ x(yc-a)=b-yd \\ \text{ divide both sides by yc-a } \\ x=\frac{b-yd}{yc-a} \\ \text{ replace y with x } \text{ and replace x with } f^{-1}(x) \\ f^{-1}(x)=\frac{b-xd}{xc-a}\]
Now I know the function I chose doesn't represent all rational functions.

Answer 3

or all one-to-one rational functions that is

Answer 4

since a rational function has to be one to one in order for the inverse function to exist

Answer 5

When factoring, you could also use the completing the square method :)