Adding and Subtracting Rational Expressions Calculator

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A rational number is something which can be expressed in the form $\frac{p}{q}$ where p and q are integers and q is not equal to zero. A rational function is made of rational numbers.

**Adding and Subtracting Rational Expressions Calculator** is helpful in calculating two rational function. It is adding rational expressions calculator that add and subtract rational numbers so called add and subtract rational numbers calculator. It is even tool of adding rational expressions with different denominators calculator and subtracting rational expressions calculator. You just have to enter the expressions and operation and get the answer instantly.

Below is given a default two rational function with the appropriate operations to be taken like addition or subtraction. If u click "Calculate", it will find the common denominator and perform the appropriate operation and get the simplified answer.

Below is given a default two rational function with the appropriate operations to be taken like addition or subtraction. If u click "Calculate", it will find the common denominator and perform the appropriate operation and get the simplified answer.

Factorize the denominator of the given expression.

Find the LCD of the denominator to get common denominator.

Multiply the numerator with expression which is not present in the denominator

Perform the operations either addition or subtraction in the numerator to get the answer.

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

**Step 1 :**$\frac{4x}{2x + 2}$ + $\frac{3}{2x + 6}$

**Step 2 :**LCD = (2x + 2)(2x +6)

**Step 3 :**$\frac{4x}{2(x+1)}$ + $\frac{3}{2(x + 3)}$ = $\frac{4x (2x + 6)}{(2x + 2)(2x +6)}$ + $\frac{3(2x + 2)}{(2x + 2)(2x +6)}$

= $\frac{8x^{2} + 24x}{(2x + 2)(2x +6)}$ + $\frac{6x + 6}{(2x + 2)(2x +6)}$

**Step 4 :**$\frac{4x}{2(x+1)}$ + $\frac{3}{2(x + 3)}$ = $\frac{8x^{2} + 24x + 6x + 6}{(2x + 2)(2x +6)}$

**Answer :**$\frac{4x}{2(x+1)}$ + $\frac{3}{2(x + 3)}$ = $\frac{8x^{2} + 30 x + 6}{(2x + 2)(2x +6)}$ = $\frac{4x^{2} + 15 x + 3}{2(x + 2)(x + 3)}$ = $\frac{4x^{2} + 15 x + 3}{2(x + 2)(x + 3)}$

$\frac{5x}{x - 3}$ - $\frac{y}{3y - 2}$

**Step 1 :**$\frac{5x}{x - 3}$ - $\frac{y}{3y - 2}$

**Step 2 :**LCD = (x - 3)(3y - 2)

**Step 3 :**$\frac{5x}{x - 3}$ - $\frac{y}{3y - 2}$ = $\frac{5x (3y - 2)}{(x - 3)(3y - 2)}$ - $\frac{y (x - 3)}{(x - 3)(3y - 2)}$

= $\frac{15xy - 10x}{(x - 3)(3y - 2)}$ - $\frac{xy - 3y}{(x - 3)(3y - 2)}$**Step 4 :**$\frac{4x}{2x+3}$ + $\frac{3}{6x + 5}$ = $\frac{15xy - 10x -xy + 3y}{(x - 3)(3y - 2)}$

**Answer :**$\frac{4x}{2x+3}$ + $\frac{3}{6x + 5}$ = $\frac{14xy - 10x +3y}{(x - 3)(3y - 2)}$

A finance company invested a sum of amount among A, B, C and D projects in the ratio of 3 : 5 : 8 : 9 respectively. If the investment amount of project D is 1872 dollars more than the investment amount of project A, then what is the total investment of project B and project C together.

**Step 1 :**Let x be the total investment among four projects, A, B, C and D.

Sum of ratio = 3 + 5 + 8 + 9 = 25**Step 2 :**According to the statement: ($\frac{9}{2 5} $ - $\frac{3} {25} $)x = 1872

**Step 3 :**Or $\frac{(9-3) x} {25} $ = 1872 (solving rational expression)

$\frac{6x}{25}$ = 1872**Step 4 :**X = $\frac{1872 \times 25} {6}$ = 7800

Total amount invested by a finance company is 7800 dollars.**Answer :**Therefore, the total amount of money invested in Project B and project C together = $\frac{5+8}{25}$ $\times$ 7800 = 4056 dollars.

Ken has two sons and both are going to write a school admission test. The ratio of their age is 5 : 1. Four years hence the ratio of the ages of elder son and younger son will be 17 : 5. How old is each one now?

**Step 1 :**Let present age of his younger son = x years.

**Step 2 :**Then present age of his elder son = 5x years

Present Age

4 Year Hence

Elder Son

5x

5x + 4

Younger Son

x

x+ 4

**Step 3 :**According to the statement: $\frac{5x + 4}{x + 4} 4 = $\frac{ 17}{ 5} $

5(5x + 4) = 17 (x + 4)

25 x + 20 = 17 x + 68

25x = 17x + 48

8x = 48

x = $\frac{48}{8}$

x = 6**Step 4 :**Present age of his elder son = 5 $\times$ 6 = 30

**Answer :**Ken’s younger son is 6 years old and elder one is 30 years old.

A man manufactured a rectangular model. One side of the model is four smaller than another. The sum of their reciprocals sides is 5/24. What are the dimensions? (Side length is an integer)

**Step 1 :**Let x is the side length of model. Then second side is of measure x – 4.

**Step 2 :**Since sum of the reciprocal sides measures = $\frac{ 5}{24 }$

i.e. $\frac{1}{x}$ + $\frac{1}{x – 4 }$ = $\frac{ 5}{24 } $

$\frac{ (x-4) + x }{x(x-4)}$ = $\frac{ 5}{24 } $

$\frac{ 2x - 4}{x(x-4)}$ = $\frac{ 5}{24 } $

5(x - 4) x = 24 (x - 4) + 24x

5x$^2$ - 20x = 48x - 96

5x$^2$ - 68x + 96 = 0**Step 3 :**Solving by factoring, we get

(x - 12) (5x - 8) = 0

x = 12 and x = $\frac{ 8}{ 5} $**Step 4 :**x = $\frac{ 8}{ 5} $ is not an integer, so neglect this value.

One side of the model is 12 units and the length of second side is (12 – 8) 4 units.**Answer :**Dimensions of the model are 12 units and 4 units.