Is this right - Math question?

Question

4
--
s

plus

7
--
s^2

= 16 [ 7 ]
---- + ---
s^2 [ s^2 ]

= 23
----
s^2

????????????????????????????

Also I need to express this equation in simplest form showing all the algebraic steps. My main goal in this equation is to solve for X

4x [ 4 ]
---- + ---------
x^2 + 18x + 72 [ x + 6 ]


:)

Answer 1

firefly already answered your first equation so I won't bother with that. For your second equation, I'm pretty sure you meant:
[(4x)/(x^2+18x+72)] + [(4)/(x+6)]

First, we have to factor out the denominator of the left fraction. We get:

[(4x)/((x+6)(x+12))] + [(4)/(x+6)]

Now, we will multiple the right fraction by (x+12)/(x+12) in order to create common denominators to add the two fractions. After multiplying the right fraction by (x+12)/(x+12), we add the two fractions to get:

(4x+4(x+12)) / [(x+6)(x+12)]

We can now distribute the numerator and simplify.

(4x+4x+48) / [(x+6)(x+12)]
(8x+48) / [(x+6)(x+12)]

This step will now backtrack a little in order to factor out the numerator to cancel out terms. We will factor out a 8.

8(x+6) / [(x+6)(x+12)]

After this, we can cross out the (x+6) term.

8 / (x+12)

There is your simplified equation. In order to solve for x, we will have to set the equation equal to 0 and solve.

8 / (x+12) = 0

However, for this equation, y=0 is an asymptote so it will never reach 0.

Answer 2

No. Remember that when finding a common denominator, you have to multiply the numerator and denominator by the same quantity -- doing otherwise will change the value of the fraction. In your problem, you multiplied the numerator by 4 and the denominator by s. Unless you're extremely lucky, s≠4, so this changes the value of the fraction. The proper method is to multiply both the numerator and denominator by s. So you have:

4/s+7/s² = 4s/s² + 7/s² = (4s+7)/s²

To simplify (4x)/(x²+18x+72) + 4/(x+6), you have:

4x/(x²+18x+72) + 4/(x+6)
Factor:
4x/((x+6)(x+12)) + 4/(x+6)
Mutiply the fraction on the right by (x+12)/(x+12):
4x/((x+6)(x+12)) + 4(x+12)/((x+6)(x+12))
Add:
(4x + 4(x+12))/((x+6)(x+12))
Distribute the 4 and simplify:
(8x+48)/((x+6)(x+12))
Factor:
8(x+6)/((x+6)(x+12))
Cancel:
8/(x+12)

Answer 3

4/s+7/s^2 = 4s/s^2 + 7/s^2 = (4s+7)/s^2
Your mistake was in squaring the first term. You can multiply by 1, but not square a term. I multiplied by 1, or, s/s, to get a common denominator.

I am not sure I understand the second equation. Is i
4x/x^2 + 4/(10x+72(x+6))?

Answer 4

Jon and Pascal are right on.