Simplify:
2/x+5 + 4/x+3 times (x+3)(x+5)/(3x+13)
I believe you mean (2/(x+5) + 4/(x+3))*(x+3)(x+5)/(3x+13)
Distribute the (x+3)(x+5)/(3x+13)
2(x+3)/(3x+13)+4(x+5)/(3x+13)
They have the same denominator, so you can add them:
(2(x+3)+4(x+5))/(3x+13)
Simplify the numerator:
(2x+6+4x+20)/(3x+13)
(6x+26)/(3x+13)
Divide by (3x+13):
2(3x+13)/(3x+13) = 2
a^+14a-51=0
To simplify the expression 2/x+5 + 4/x+3 times (x+3)(x+5)/(3x+13), you can follow these steps:
Step 1: Simplify the individual terms:
a) For 2/x+5:
- This is a fraction with a constant numerator (2) and a binomial denominator (x+5).
- To simplify, you do not perform any operations further, as it is already in the simplest form.
b) For 4/x+3:
- Similar to the previous term, this is a fraction with a constant numerator (4) and a binomial denominator (x+3).
- Again, the fraction is already in the simplest form.
c) For (x+3)(x+5)/(3x+13):
- This is a fraction with a quadratic numerator (x+3)(x+5) and a linear denominator (3x+13).
- Distribute the quadratic numerator:
(x+3)(x+5) = x^2 + 8x + 15
- So the fraction becomes:
(x^2 + 8x + 15)/(3x+13)
Step 2: Multiply the terms together:
- Now that all terms are simplified, multiply them together:
(2/x+5) * (4/x+3) * (x^2 + 8x + 15)/(3x+13)
Step 3: Simplify the combined expression:
- To simplify the expression further, you need to find the least common denominator (LCD) for all the terms involved. However, since there is no common factor between them, you cannot simplify this expression any further.
So, the simplified expression is:
(2/x+5) * (4/x+3) * (x^2 + 8x + 15)/(3x+13)