a We must solve all of the given rational expressions. For the first problem, the fractions have the same denominator. Add the numerators and factor out Giant Ones.
The denominator in the second fraction is a difference of squares. We can use that to factor it.
(x+3)(x-4)/(3x+1)(x-4)*(3x+1)(x-7)/x^2-9
Let's factor the fourth expression.
Similar to the previous exercise, we want to factor each polynomial before carrying out the division. First, let's do the numerator in the first fraction.
2x^2+8x-10/2x^2+15x+25Ă·4x^2+10x-24/2x^2+x-10
Let's factor the first expression.
Now we substitute the factored forms into the original expression and divide.
2(x+5)(x-1)/(2x+5)(x+5)Ă·4(x+6)(x-1)/(2x+5)(x-2)
Remember that when dividing two fractions, the fraction in the denominator is inverted and multiplied by the numerator.
d To subtract two fractions they need to have the same numerator. 7/x+5-4-6x/x^2+10x+25
These don't. Let's factor the second denominator and see if we can find a common denominator.
Now we notice that by multiplying the denominator in the first fraction by (x+5) the fractions get the same denominator. But we have to multiply the numerator with the same factor to make sure that we do not change the original expression.
