𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Evaluate (4(45!)+46!)/150(44!)

𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

First, let's simplify the numerator:

4(45!) + 46!

Recall that 46! = 46 × 45!

So, the numerator becomes:

4(45!) + 46 × 45!

Factor out 45!:

(4 + 46) × 45! = 50 × 45!

Now, let's look at the denominator:

150(44!)

We need to relate 45! to 44!. Recall that 45! = 45 × 44!

Now, divide the numerator by the denominator:

(50 × 45!) / (150 × 44!)

Substitute 45! = 45 × 44!:

(50 × 45 × 44!) / (150 × 44!)

Cancel out 44! from the numerator and the denominator:

(50 × 45) / 150

Simplify the expression:

(50 × 45) / (3 × 50) (since 150 = 3 × 50)

Cancel out 50 from the numerator and the denominator:

45 / 3 = 15

Therefore, (4(45!) + 46!) / (150(44!)) = 15.