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,

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

**Example 2**: Simplify

`\frac{5x+10}{5}`

**Solution:**

We have,

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,

**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}\\

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