Answer:
25
Step-by-step explanation:
Answer:
![x=7](https://tex.z-dn.net/?f=x%3D7)
Step-by-step explanation:
Hi there!
![-2^2(-5x+10)=100](https://tex.z-dn.net/?f=-2%5E2%28-5x%2B10%29%3D100)
Solve -2^2:
![-4(-5x+10)=100](https://tex.z-dn.net/?f=-4%28-5x%2B10%29%3D100)
Divide both sides by -4:
![\displaystyle \frac{ -4(-5x+10)}{-4}=\frac{100}{-4} \\\\-5x+10=-25](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%20-4%28-5x%2B10%29%7D%7B-4%7D%3D%5Cfrac%7B100%7D%7B-4%7D%20%5C%5C%5C%5C-5x%2B10%3D-25)
Subtract 10 from both sides:
![-5x+10-10=-25-10\\-5x=-35](https://tex.z-dn.net/?f=-5x%2B10-10%3D-25-10%5C%5C-5x%3D-35)
Divide both sides by -5:
![\displaystyle \frac{-5x}{-5} = \frac{-35}{-5} \\\\x=7](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B-5x%7D%7B-5%7D%20%3D%20%5Cfrac%7B-35%7D%7B-5%7D%20%5C%5C%5C%5Cx%3D7)
Therefore, x = 7.
I hope this helps!
All ambitious So rude and always negative
Answer:49
Step-by-step explanation:
Answer:
![\frac{3x+6}{x^{2}-x-6 } +\frac{2x}{x^{2} +x-12}=\frac{5x+12}{x^{2} +x-12}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B6%7D%7Bx%5E%7B2%7D-x-6%20%7D%20%2B%5Cfrac%7B2x%7D%7Bx%5E%7B2%7D%20%2Bx-12%7D%3D%5Cfrac%7B5x%2B12%7D%7Bx%5E%7B2%7D%20%2Bx-12%7D)
Step-by-step explanation:
The given expression is
![\frac{3x+6}{x^{2}-x-6 } +\frac{2x}{x^{2} +x-12}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B6%7D%7Bx%5E%7B2%7D-x-6%20%7D%20%2B%5Cfrac%7B2x%7D%7Bx%5E%7B2%7D%20%2Bx-12%7D)
First, we need to factor each part of the expression
![\frac{3(x+2)}{(x+2)(x-3)} +\frac{2x}{(x-3)(x+4)}](https://tex.z-dn.net/?f=%5Cfrac%7B3%28x%2B2%29%7D%7B%28x%2B2%29%28x-3%29%7D%20%2B%5Cfrac%7B2x%7D%7B%28x-3%29%28x%2B4%29%7D)
Remember that quadractic expression are factored in two binomial factors. The first quadratic expression factors are about two numbers which product is 6 and which difference is one. The second quadratic expression is about two numbers which product is 12 and which difference is 1.
Now, we simplify equal expression at each fraction.
![\frac{3}{(x-3)} +\frac{2x}{(x-3)(x+4)}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B%28x-3%29%7D%20%2B%5Cfrac%7B2x%7D%7B%28x-3%29%28x%2B4%29%7D)
Then, we use the least common factor about the denominators to sum those fractions. In this case, the least common factor is
, because those are the factors present in the denominators.
Now, we divide each fraction by the least common factor, and then multiply the numeratos by its result.
![\frac{3(x+4)+2x}{(x-3)(x+4)}](https://tex.z-dn.net/?f=%5Cfrac%7B3%28x%2B4%29%2B2x%7D%7B%28x-3%29%28x%2B4%29%7D)
Finally, we multiply all products and sum like terms.
![\frac{3x+12+2x}{x^{2} +4x-3x-12}=\frac{5x+12}{x^{2} +x-12}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B12%2B2x%7D%7Bx%5E%7B2%7D%20%2B4x-3x-12%7D%3D%5Cfrac%7B5x%2B12%7D%7Bx%5E%7B2%7D%20%2Bx-12%7D)
Therefore, the sum of the initial expression is equal to
![\frac{5x+12}{x^{2} +x-12}](https://tex.z-dn.net/?f=%5Cfrac%7B5x%2B12%7D%7Bx%5E%7B2%7D%20%2Bx-12%7D)