Question

How do you multiply\[\dfrac{{7x}}{{5x + 15}}.\dfrac{{x + 3}}{8}\] ?

Answer 1

Hint:Here in the above question we are asked to multiply the rational expressions and it is almost the same as multiplying fractions. So firstly we will simplify the equation by factoring to take out common terms in order to make calculation easier. Now to find out the product we will multiply numerator with numerator while denominator with denominator. We can even simplify the product of rational expressions if required.

Formula used:
The formula used in the above equation is,
\[\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{{ac}}{{bd}}\]
Where we will multiply the numerator with numerator and denominator with denominator after factorization in order to simplify

Complete step by step answer:
Firstly we need to factorize the algebraic fractions wherever it can be done. So in this equation we can factor \[5\] from the denominator of the first fraction. So it becomes
\[5x + 15 = 5(x + 3)\]
Now rewrite the equation with this factorization
\[\dfrac{{7x}}{{5(x + 3)}}.\dfrac{{x + 3}}{8}\]
Lastly after cross simplification we will get
\[\dfrac{{7x}}{{5.8}} \\
\therefore\dfrac{{7x}}{{40}} \\ \]
So the final answer after multiplying the equation is \[\dfrac{{7x}}{{40}}\].

Additional information:
While calculating the product of two given fractions we should remember that the product of the numerators of the given fractions is the numerator and denominator is the product of the denominators of the given fractions.

Note:When we solve the given equation we will see that rational expressions will not be given in factored form so firstly we will factorize all numerators and denominators completely in order for making our calculation simpler and easier. Then we will multiply and if there are any common factors then we will cancel it. While solving such equations leaving answers in factored form is considered as best practice.