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Rational Expressions Calculator
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Rational Expressions Calculator (or Simplify Rational Expressions Calculator) is a rational calculator that finds the factors of a rational expression. If takes a rational expression and simplifies it so called as simplifying rational expressions calculator. You just have to enter the numerator and denominator in the block provided get the simplified answer with our rational expressions solver.

Below is given a default rational expressions, you could see how to simply using this calculator.

 

Steps for Rational Expressions Calculator

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Step 1 :  

Factor both the denominator and numerator seperately.



Step 2 :  

Divide common factors of the fractions.



Step 3 :  

Rewrite the remaining expressions.



Problems on Rational Expressions Calculator

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  1. Solve $\frac{x^2+5x+6}{ x^2+5x+6}$.


    Step 1 :  

    In the above expression, both numerator and denominator are same.


    So factors of x2+5x+6 = (x+2)(x +3)



    Step 2 :  

    Now $\frac{x^2+5x+6}{ x^2+5x+6}$ =  (x+2)(x+3)/(x+2)(x+3) = 1



    Step 3 :  

    After solving given expression we are left with 1.



    Answer  :  

    1.



  2. Solve $\frac{(x-1)(x^2+4x+3)}{x^2+3x-4}$.


    Step 1 :  

    Numerator = (x-1)(x2+4x+3)


    Here x2+4x+3 is a quadratic polynomial. Lets apply factorization method to find its factors.


    x2+4x+3 = x2+(3+1) x +3 (Split mid term as (3+1)x = 4x)


    = x2+ 3x +  x +3


    = x(x + 3) + (x + 3)


    =(x + 1)(x + 3)


    Factors of numerator are (x-1)(x + 1)(x + 3)


    Now denominator = x2+3x-4 = x2+ (4 - 1) x-4


    = x2+ 4x - x-4


    = x(x + 4) - (x + 4)


    =(x-1)(x+4)


    Factors of denominator are (x-1)(x+4)



    Step 2 :  

    Eliminate  the common  factors. From above we can see that (x-1) is common in both numerator and denominator.

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



    Answer  :  

    $\frac{(x+3)(x+1)}{(x+4)}$.



  3. The owner of a women's accessories store charges his customers 12 % more than the cost price. If Marry paid 448 dollars for a bag. What is the cost price of the bag.


    Step 1 :  

    Let x be the cost price of a bag.



    Step 2 :  

    Marry paid for a bag = 448 dollars
    Shopkeeper charges 12 % more than the cost price, it means she paid 112 % of x.



    Step 3 :  

    So 112 % of x = 448
    Or $\frac{112}{100}$ $\times$ x = 448
    Reduce $\frac{112x}{100}$ into simplest form using calculator, which is $\frac{28x}{25}$
    Now $\frac{28x}{25}$ = 448
    X = $\frac{448 \times 25}{28} $ = 400



    Answer  :  

    The cost price of the bag is 400 dollars.



  4. There are two companies A and B. Both are manufacturing computers and laptops. Company A produces 10/15 th of the products produces by company B. Company A produces a total of 450 products in a month. What is the total number of computers and laptops produced by company B in the same period?


    Step 1 :  

    Total products produced by company A = 450


    Let Number of products produce by company B = x



    Step 2 :  

    Also we are given with, Number of products produce by company A = $\frac{10}{15}$ x



    Step 3 :  

    450 =  $\frac{10}{15}$ x


    450 = $\frac{2}{3}$ x


    x = $\frac{450 \times 3}{2}$


    x = 675



    Answer  :  

    Company B produced 675 products (computers and laptops) in one month.



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