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Multiplying and Dividing Rational Expressions Calculator
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A rational function is something which is made up of rational numbers. Multiplying and Dividing Rational Expression calculator (multiplying rational expressions calculator) helps you to Multiply or divide the rational functions. It can simply be called multiplying rational expressions calculator that gives the answer. You just have to enter rational expressions and get the answer hence known as rational expressions calculator.

Below is given two default rational expressions with the appropriate operation, click "Calculate". It divides or multiplies the rational expression according to the operation and factorize the terms in numerator and denominator and get the final answer.

## Steps for Multiplying and Dividing Rational Expressions Calculator

Step 1 :

Observe the problem and see whether to divide the rational function or multiply. If you have to divide the function then firstly take the reciprocal of denominator and multiply with the numerator of the given expression. If you need to multiply the rational function keep the expression as it is and proceed for the next step.

Step 2 :

Factorize the terms present in numerator and denominator.

Step 3 :

Simplify the factorized product by dividng the common factors present in numerator with the denominator

Step 4 :

Finally multiply the terms in numerator as well as denominator to get a final answer.

## Problems on Multiplying and Dividing Rational Expressions Calculator

1. ### $\frac{\frac{x^{2} + 5x + 4}{x + 1}}{\frac {x}{(x + 3)}}$

Step 1 :

$\frac{\frac{x^{2} + 5x + 4}{x + 1}}{\frac {x}{(x + 3)}}$
= $\frac{x^{2} + 5x + 4}{x + 1}$ $\times$ $\frac{x + 3}{x}$

Step 2 :

$\frac{\frac{x^{2} + 5x + 4}{x + 1}}{\frac {x}{(x + 3)}}$ = $\frac{(x+4)(x+1)}{x+1}$ $\times$ $\frac{x + 3}{x}$

Step 3 :

$\frac{\frac{x^{2} + 5x + 4}{x + 1}}{\frac {x}{(x + 3)}}$ = $\frac{(x + 4)(x + 3)}{x}$

Step 4 :

$\frac{\frac{x^{2} + 5x + 4}{x + 1}}{\frac {x}{(x + 3)}}$ = $\frac{x^{2} + 3x + 4x + 12}{x}$

$\frac{x^{2} + 7x + 12}{x}$

2. ### $\frac{x^{2} - 9}{x}$ $\times$ $\frac{x^{2}}{x + 3}$

Step 1 :

Since it is multiplication, no change is done to the problem in this step.

Step 2 :

$\frac{x^{2} - 9}{x}$  $\frac{x^{2}}{x + 3}$ = $\frac{(x + 3)(x - 3)}{x}$ $\frac{x^{2}}{(x + 3)}$

Step 3 :

$\frac{x^{2} - 9}{x}$  $\frac{x^{2}}{x + 3}$ =   x(x - 3)

Step 4 :

$\frac{x^{2} - 9}{x}$  $\frac{x^{2}}{x + 3}$ = x2 - 3x

x2 - 3x

3. ### Some college students went for river rafting. They found that,  boat travels 30 miles up a river in the same amount of the time it takes to travel 50 miles down the same river. If the current is 5 miles per hour, what is the speed of the boat in still water.

Step 1 :

Let x be the speed of the boat in still water. Then x - 5 must be its upstream and x + 5 must be the downstream.

Step 2 :

Also we know that, the equation of rate is, t = $\frac{d}{r}$

for d = 50, r = x - 5, the value of t = 30/(x-5)

for d = 30, r = x + 5, the value of t = 50/(x+5)

Step 3 :

Since time for the trip upstream =  Time for the trip downstream

Step 4 :

50 /(x+5) = 30/(x-5)

50(x – 5) = 3(x + 5)

50x - 250 = 30x + 150

50x – 30x = 400

20x = 400

x = 20