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tester [92]
3 years ago
7

Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!​

Mathematics
1 answer:
Greeley [361]3 years ago
6 0

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

\frac{3}{x + 4}  - \frac{1}{x + 3}  = \frac{x + 9}{(x^2 + 7x + 12)}

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

\frac{3*(x + 4)}{x + 4}  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

3  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x + 3)

3*(x + 3)  - \frac{(x + 4)*(x+3)}{x + 3}  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

3*(x + 3)  - (x + 4)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

(2*x + 5)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x^2 + 7*x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = (x + 9)*(x + 4)*(x+3)

Now we need to solve this:

we will get

2*x^3 + 19*x^2 + 59*x + 60 =  (x^2 + 13*x + 3)*(x + 3)

2*x^3 + 19*x^2 + 59*x + 60 =  x^3 + 16*x^2 + 42*x + 9

Then we get:

2*x^3 + 19*x^2 + 59*x + 60 - (  x^3 + 16*x^2 + 42*x + 9) = 0

x^3 + 3x^2 + 17*x + 51 = 0

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

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vodomira [7]
X= weight of TV
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3x+5y= 62.5
3x+ 2y= 52
You can either solve for a variable, or eliminate a variable by subtracting the second equation from the first:

3x + 5y = 62.5
-(3x+2y = 52)
0 + 3y = 10.5, so y = 10.5/3 or 3.5.

Now plug y= 3.5 back into any equation to get x:

3x + 5(3.5) = 62.5
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3x = 45
x = 15
Always check work. Both equations should be true for x=15, y= 3.5
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3 years ago
This is kind of off topic for math but I still need to know the answer, so I’ve finished all my math work and I know my work is
Mariulka [41]

Answer:

email or call or talk to your teacher and ask why

Step-by-step explanation:

6 0
3 years ago
Least common multiple of 2,7, and 13
san4es73 [151]


To work out the LCM, we need their prime factors. So:

2 is simple 2 x 1.

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They all have in common "1" - so we keep that aside as 1 figure, rather than 3.

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~FabSafxo

6 0
3 years ago
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bulgar [2K]

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3 years ago
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Y=-0.05x^2+4.5x-6.5 pls help to solve
givi [52]
Following with the extra hint that x = 82.03 m

There are 2 ways to approach the question, but although I prefer to group up x first before plugging value, having that -0.05x^2 to group up is too annoying:

Plug x = 82.03

=> Y = -0.05*(82.03^2) + 4.5*82.03 - 6.5
         = -336.446045 + 369.135 - 6.5
         = 26.188955 m

Please take the time and understand the answer instead of just looking at the final result.

Also I know the number is very long, but that's the question's fault. <span>¯\_(ツ)_/¯</span>

6 0
3 years ago
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