Question

What is the least common denominator for rational expression?

Answer 1

`\large \bf \implies{(x - 6)^(2)(x + 1) }`

Explanation:

`\sf \longrightarrow\frac{1}{ {x}^(2) - 5x - 6} \: and \: \frac{1}{ {x}^(2) - 12 + 36 } \\`

`\sf \longrightarrow \frac{1}{ {x}^(2) - 5x - 6 } = (1)/((x - 6)(x + 1)) \\ \\ \sf \: and \\ \\ \sf \longrightarrow \frac{1}{ {x}^(2) - 12x + 36 } = (1)/((x - 6)(x - 6))`

`\sf \longrightarrow (1)/((x - 6) ^(2)(x + 1) ) \\`

Therefore, the least common denominator is (x - 6)²(x+1).

Additional information:

# How to solve middle splitting term ?

Step 1) : First of all notice that term is in standard form.

For eg :- 6x + 2x² + 5 = 2x² + 7x + 5

Step 2) : Multiply with first and last term.

2 × 5 = 10

Step 3) : Next we have multiply got the answer 10 and subtract or add we have got the answer 7.

• 1 × 10 = 10 and 10 - 1 = 9 or 10 + 1 = 11
• 2 × 5 = 10 and 5 - 2 = 3 or 5 + 2 = 7

Now, we have got the term. We have multiply 2 and 5 got the answer 10 and we have add got the answer 7.

Step 4) : Attach the factor into the removal of 7x

2x² + 5x + 2x + 5

Step 5) : Simplify it

• 2x² + 5x + 2x + 5
• x(2x + 5) + 1(2x + 5)
• (2x + 5)( x + 1)

Step 6) : We have got the answer

`\sf \longrightarrow(2x + 5)(x + 1)`