Question

Rational functions. Adding and subtracting. Math3

Answer 1

1. The addition of two rational functions:
`$(x+2)/(x-3)+(5)/(x-1)$` is
`(x^2-x+5)/((x-3)(x-1))]`.

2. The subtraction of two rational functions:
`$(6x)/(x-5)-(5x)/(x-6)$` is
`(x)/((x-5)(x-6))`.

The image you sent shows two examples of rational functions. A rational function is any function that can be expressed as a fraction of two polynomials.

It is a function of the form P(x) / Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero.

1. The addition of two rational functions:
`$(x+2)/(x-3)+(5)/(x-1)$`.

To add these two functions, we need to find a common denominator. In this case, the common denominator is (x-3)(x-1).

Once we have the common denominator, we can simply add the numerators:

`\[((x+2)(x-1) + 5(x-3))/((x-3)(x-1)) = (x^2-x+5)/((x-3)(x-1))\]`

2. The subtraction of two rational functions:
`$(6x)/(x-5)-(5x)/(x-6)$`. Again, we need to find a common denominator.

In this case, the common denominator is
`$(x-5)(x-6)$`.

Once we have the common denominator, we can simply subtract the numerators:

`\[(6x(x-6) - 5x(x-5))/((x-5)(x-6)) = (x)/((x-5)(x-6))\]`