# What is the simplified form of 3/(4x + 3) + 21/(8x^{2} + 26x + 15)

**Solution:**

**Step 1:**

First we need to factorise 8x^{2} + 26x + 15 so that LCM is possible to take for both the terms.

On factorising the term 8x^{2} + 26x + 15 by factorization method,

The factors of product 120(8 × 15) are:

20 and 6

So that 20 + 6 gives a middle term that is 26,

which is the rule of factorization of quadratic equation

**Step2:**

⇒ 3/(4x + 3) + 21 / (8x^{2} + 26x + 15)

= 3/(4x + 3) + 21/(2x + 5)(4x + 3)

In the first term only 4x + 3 is the term in the denominator which is need to multiplied by (2x + 5) with both numerator and denominator

⇒3/(4x + 3) + 21/(2x + 5)(4x + 3)

= [3(2x + 5)/(4x + 3)(2x + 5)] + [21/(2x + 5)(4x + 3)]

**Step3:**

After taking LCM for both the terms

⇒ 3/(4x + 3) + 21/(2x + 5)(4x + 3) = [3(2x + 5) + 21 ] / (4x + 3)(2x + 5)

⇒ 3/(4x + 3) + 21/(2x + 5)(4x + 3) = [6x + 15 + 21 ]/(4x + 3) (2x + 5)

⇒ 3/(4x + 3) + 21/(2x + 5)(4x + 3) = [6x + 36 ]/(4x + 3)(2x + 5)

⇒ 3/(4x + 3) + 21/(2x + 5)(4x + 3) = 6(x + 6)/(4x + 3)(2x + 5)

**Therefore, the simplified form is 6(x + 6)/(4x + 3)(2x + 5)**

## What is the simplified form of 3/(4x + 3) + 21/(8x^{2} + 26x + 15)

**Summary :**

The simplified form of 3/(4x + 3) + 21/(8x^{2} + 26x + 15) is 6(x + 6)/(4x + 3)(2x + 5). Since it is not possible to do further simplification 6(x + 6)/(4x + 3)(2x + 5) is the simplified form of the given expression.