1.(Y+2)/(Y^2-9) * (4Y+12)/(3Y+6) ÷ 8/(2Y-6) =
2.(4X-Y)/(X+Y) * (X^2-Y^2)/(16X^2-Y^2) ÷ (2X-2Y)/(16X+4Y) =
3.(X^2-25)/(2X+12) * (X^2+8X+12)/(4X-20) ÷ (X^2+7X+10)/8X =
To solve these expressions, follow these steps:
1. Simplify the expression inside each pair of parentheses separately.
2. Multiply the numerators of the two fractions in the numerator.
3. Multiply the denominators of the two fractions in the numerator.
4. Decide whether to simplify further or leave the expression as is.
Let's apply these steps to solve the given expressions.
1. (Y+2)/(Y^2-9) * (4Y+12)/(3Y+6) ÷ 8/(2Y-6)
Step 1: Simplify the expression inside each pair of parentheses separately.
(Y+2) can't be simplified further.
(Y^2-9) can be factored as (Y+3)(Y-3).
(4Y+12) can be factored as 4(Y+3).
(3Y+6) can be factored as 3(Y+2).
8 can be factored as 2*2*2.
(2Y-6) can be factored as 2(Y-3).
Step 2: Multiply the numerators of the two fractions in the numerator.
(Y+2) * (4Y+12) = 4Y^2 + 16Y + 8Y + 24 = 4Y^2 + 24Y + 24
Step 3: Multiply the denominators of the two fractions in the numerator.
(Y^2-9) * (3Y+6) = (Y+3)(Y-3) * 3(Y+2) = 3(Y+3)(Y-3)(Y+2)
Step 4: Divide both by the denominator.
(4Y^2 + 24Y + 24) / [3(Y+3)(Y-3)(Y+2) * (2(Y-3))]
Therefore, the first expression simplifies to:
(4Y^2 + 24Y + 24) / [6(Y+3)(Y+2)(Y-3)(Y-3)]
2. (4X-Y)/(X+Y) * (X^2-Y^2)/(16X^2-Y^2) ÷ (2X-2Y)/(16X+4Y)
The steps remain the same as above. Simplify each expression inside parentheses.
3. (X^2-25)/(2X+12) * (X^2+8X+12)/(4X-20) ÷ (X^2+7X+10)/8X
Again, the steps remain the same as above. Simplify each expression inside parentheses.
By following these steps, you can simplify and evaluate the given expressions.