Q. Simplify. Express your answer as a single fraction in simplest form. 3x+wx35
Identify common denominator: Identify the common denominator.To add the fractions3x and wx35, we need to find a common denominator. The least common denominator (LCD) for 3 and wx3 is 3wx3.
Rewrite with common denominator: Rewrite each fraction with the common denominator.We need to adjust each fraction so that they both have the common denominator of 3wx3.For the first fraction, 3x, we multiply the numerator and denominator by wx3 to get 3⋅wx3x⋅wx3.For the second fraction, wx35, we multiply the numerator and denominator by 3 to get wx3⋅35⋅3.
Perform multiplications: Perform the multiplications.Now we perform the multiplications from Step 2.For the first fraction, (x⋅wx3)/(3⋅wx3) simplifies to (wx4)/(3wx3).For the second fraction, (5⋅3)/(wx3⋅3) simplifies to 15/(3wx3).
Combine fractions: Combine the fractions.Now that both fractions have the common denominator, we can combine them.(wx4)/(3wx3)+15/(3wx3)=(wx4+15)/(3wx3)
Simplify numerator: Simplify the numerator.We can't simplify wx4+15 any further, so the numerator remains as is.3wx3wx4+15
Simplify fraction: Simplify the fraction.We look for any common factors in the numerator and denominator that can be canceled out. In this case, there are no common factors to cancel.(wx4+15)/(3wx3) is already in simplest form.
More problems from Add and subtract rational expressions