Etta W. answered • 06/16/20
experienced math tutor for all ages
To add fractions, we need to find the least common denominator(LCD)..
the denominators are x and 4x.. The LCD is 4x.
the first fraction has a denominator of x so we will multiply that denominator by 4 to have equal denominators. We need to multiply 5, the numerator, by 4 so that we have an equivalent fraction.
The first fraction will now be 20/4x which can added to 3/4x. Once the denominators are equal, we add the numerators which are 20 and 3. The new numerator is 23. The denominator remains the same. the answer is 23/4x. The restriction is that x cannot be equal to zero since division by zero is impossible.
(b) To accomplish division with fractions, we use Keep, Change, Flip.
Keep the first fraction, Change the division sign to multiplication, and Flip (invert) the second fraction. Next we need to factor the expressions on the first fraction.
The numerator has a greatest common factor (GCF) of x which will give us x(x-5).
The denominator will factor to (x-5)(x+6).. We can reduce that to x/(x+6) which will be multiplied by (x+6)/2x^2. We can cancel the (x+6). Now we have x/2x^2. which will then simplify to 1/2x. the restriction is x cannot be equal to zero.
