Next, we will rewrite the denominator in the second fraction. Notice that we will substitute the denominator in the first fraction with its factored form.
The fractions have now been added. Since it is not possible to factor out a common factor in the numerator, we cannot simplify the fraction. However, we can simplify the numerator if we distribute and multiply the parentheses.
b We are given the difference between two rational expressions.
4x^2-11x+6/2x^2-x-6 - x+2/2x+3
The first step is to rewrite the fractions so that they have the same denominator. Since the first denominator is a quadratic trinomial, we can try to factor it.
To get the same denominator, we need to expand the second fraction with (x-2). Notice that we will substitute the denominator in the first fraction with its factored form.
c Since the numerator and denominator are in factored form already, we can carry out the division straight away. Dividing two fractions is the same thing as multiplying the first one with the second fraction's reciprocal.
d We want to multiply the given rational expressions.
2m^2+7m-15/m^2-16*m^2-6m+8/2m^2-7m+6
Before we multiply the fractions, we want to factor each expression to make the multiplication easier. Let's start with the numerator in the first fraction.
