Algebra with fractions is a representation of algebraic expression in simple fraction form as numerator and denominator. In an algebra fraction, when we are adding or subtracting, one thing we need to keep in mind is that it should have a common denominator by cross multiplying.

In this article we will be solving few problems related to Algebra with fractions in order to get better understanding about it.

Examples 1: Simplify

\frac{1}{(x + 2)}+ \frac{6}{(x + 10)}

Solution:


We have,

\frac{1}{(x + 2)}+ \frac{6}{(x + 10)} \\ =\frac{ 1(x + 10) + 6(x + 2)}{(x + 2)(x + 10)}      (by Cross Multiplying)\\ =\frac{x + 10 + 6x + 12}{(x + 2)(x + 10)}\\ = \frac{7x + 22}{(x + 2)(x + 10)}

Hence, after simplification we get \frac{7x + 22}{(x + 2)(x + 10)}

 

Example 2: Simplify

\frac{5x+10}{5}

Solution:

We have,

\frac{5x+10}{5}

Here, the common factor of 5

=\frac{5(x+2)}{5}

=x+2
So, after simplification we get x+2

Example 3: Reduce

\frac{4x^4}{2x^2}

Solution:

We have,

\frac{4x^4}{2x^2} =\frac{2x^2(2x^2)}{2x^2}           (after cancelling)\\    =2x^2 Therefore, after reducing the answer is 2x^2

Solve Equation of Algebra with fractions

 Example 1: Solve

\frac{1}{x+4}=\frac{1}{2}

 Solution:  

\frac{1}{x+4}=\frac{1}{2}

(1)(2)=(1)(x+4)
2=x+4
x= -2
As a result, the value of x= -2

Example 2: Solve

\frac{1}{(x + 2)}+ \frac{6}{(x + 10)} =\frac{4}{3}\\       

Solution:

\frac{ 1(x + 10) + 6(x + 2)}{(x + 2)(x + 10)}=\frac{4}{3}\\

\frac{x + 10 + 6x + 12}{(x + 2)(x + 10)}=\frac{4}{3}\\ 3 (7x + 22)=4(x + 2)(x + 10)\\ 21x+66=4(x^2+10x+2x+20)\\ 4x^2+48x-21x+80-66=0\\ 4x^2+27x+14=0\\ x=\frac{-b±\sqrt{b^2-4ac}}{2a}\\ =\frac{-27±\sqrt{27^2-4(4)(14)}}{2(4)}\\  =\frac{-27±\sqrt{729-224}}{8}\\  =\frac{-27±\sqrt{505}}{8}\\  =\frac{-27±22\sqrt{21}}{8}

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