perform indicated operations.
(a+3)/(5a+25)-(a-1)/(3a+15)
(a+3)/5(a+5)-(a-1)/3(a+5)=(a+3)5(a+5)/5(a+5)3(a+5)-(a-1)5(a+5)/5(a+5)3(at5)= 5a^2+25a+15a+75+5a^2+25a-5a-25/5(a+5)3(a+5)
i got (10a^2+60a-50)/5(a+5)3(a+5)and that's wrong. where did i go wrong?
(a+3)/(5a+25)-(a-1)/(3a+15)
(a+3)/5(a+5)-(a-1)/3(a+5)
=(a+3)3(a+5)/5(a+5)3(a+5)-(a-1)5(a+5)/5(a+5)3(a+5)
Aside from that, I'd not include (a+5) twice, making it
=3(a+3)/15(a+5) - 5(a-1)/15(a+5)
= (3a+9-5a+5)/15(a+5)
= 2(7-a)/15(a+5)
Since the a+5 is already common, you don't need it twice
LCD = 15(x+5)
so your second line
= 3(a+3)/(15(a+5)) - 5(a-1)/(15(a+5))
= (3a+9 - 5a + 5)/(15(a+5))
= (-2a + 14)/(15(a+5))
=-2(a-7)/(15(a+5))
To identify where you went wrong in your calculations, let's go through step by step.
Starting from the given expression:
(a+3)/(5a+25) - (a-1)/(3a+15)
First, we need to find the common denominator for both fractions. In this case, the common denominator is (5a+25)(3a+15), which can also be written as 5(a+5)(3a+5):
[(a+3)(3a+15)]/[(5a+25)(3a+15)] - [(a-1)(5a+25)]/[(3a+15)(5a+25)]
Now, let's simplify each numerator:
[(a+3)(3a+15)] = (a+3)3(a+5) = 3(a+3)(a+5)
[(a-1)(5a+25)] = (a-1)5(a+5) = 5(a-1)(a+5)
Plugging these simplified numerators back in, the expression becomes:
[3(a+3)(a+5)]/[(5a+25)(3a+15)] - [5(a-1)(a+5)]/[(3a+15)(5a+25)]
Next, we can combine the fractions using the common denominator:
[3(a+3)(a+5) - 5(a-1)(a+5)]/[(5a+25)(3a+15)]
Simplifying further, we expand the terms inside the brackets:
[3(a^2+8a+15) - 5(a^2+4a-5)]/[(5a+25)(3a+15)]
Now distribute the numbers outside the brackets:
[3a^2+24a+45 - 5a^2-20a+25]/[(5a+25)(3a+15)]
Combine the like terms:
[-2a^2 + 4a + 70]/[(5a+25)(3a+15)]
Therefore, the correct answer is (-2a^2 + 4a + 70)/[(5a+25)(3a+15)].