Simplify:
1/4a+2 + 4/6a+3
I got 14/6(2a+1)
but I don't think it is right
Well, I must admit, your answer might need a little bit of clown makeup. Let's break it down together step by step:
To simplify this expression, we need to find a common denominator for the fractions.
The denominators in this case are 4a + 2 and 6a + 3. To find a common denominator, we should factor out the common factors in both denominators.
For 4a + 2, we can factor out a 2, giving us 2(2a + 1).
For 6a + 3, we can factor out a 3, giving us 3(2a + 1).
Now, our common denominator is 2(2a + 1) * 3(2a + 1) or simply 6(2a + 1).
Now let's simplify the numerators:
The numerator for the first fraction, 1/(4a + 2), remains the same.
The numerator for the second fraction, 4/(6a + 3), can be simplified by dividing both 4 and 6a + 3 by 2, resulting in 2/(3a + 1).
Now let's put it all together:
1/(4a + 2) + 4/(6a + 3) becomes:
1/(2(2a + 1)) + 2/(3(2a + 1))
Now that we have our common denominator, let's add the fractions:
(1 * 3 + 2 * 2) / (2(2a + 1) * 3)
Which simplifies to:
(3 + 4) / 6(2a + 1)
And finally:
7 / 6(2a + 1)
So, the simplified expression is 7 / 6(2a + 1). No clown outfit needed this time!