Question
Solve each equation.$$ rac{k}{k^{2}-6 k-16}- rac{12}{5 k^{2}-65 k+200}= rac{28}{5 k^{2}-15 k-50}$$
Solve each equation. $$ \frac{k}{k^{2}-6 k-16}-\frac{12}{5 k^{2}-65 k+200}=\frac{28}{5 k^{2}-15 k-50} $$
Answers
Use the quadratic formula to solve each equation.
$$
4 k^{2}=5 k+2
$$
So you're solving the following equation. We have 16 case. Where'd must one equals Negative eight king. So one way to do this again is to make all this pass it over to this side. So this is gonna be 16 k squared, plus one plus k equals to Syria. Now we have a tragic factor out if you want, or you could use the quadratic formula. So in this case, it's K e course. Negative B No, sir. My nest square, the square minus four A. C. Well, you are so drinks a So then you re write this so that it's an ABC Or you could just label. This is a This is be in this sissy. Remember, C is for Constance of us. Your number This way. It's up. So this is gonna be negative. Eight. No ser minus square would, uh, eight squared minus four, tying 16 times one or were two times 16. So simplify this. This is going to become negative. Eight, Mr. Minus square root off 64 minus. And then this time I do have to keep the minus because I don't have one negative and 16 tens. War. Give me 64. And then the bottom part is 32. So this is simplified Tonegative. A plus or minus. This is several. So this part is gone. You don't have it anymore over there too. So you actually have only one solution. Which iss? All right. K equals Negative Inc over 32. And recent. We can simplify this by dividing by eight. So this is going to negative one over for So they divided by eight. Then to your answers. Negative 1/4 or the safety s negative. 0.25.
To solve this equation. The first thing I want to do is distribute. So distribute the four and also distribute the negative one. So my next line he gave me careful in your distributed at negative one two B minus two. Now I want to just want to combine my life terms so I can combine my case for K minus three k gives me one K, which is just the same as K. And then I have negative 24 minus two so that negative 24 is not 24 minus two. It's negative. 24 minus two gives me negative 26. Now I would do the opposite operation. I'm trying to, um, talking, right, trying to isolate the K. So I'm going to add 26 and I get k equals positive 21 to check. I'm going to substitute 21. And everywhere there's a K So three times 21 would be 63. So we get four times. Subtract first in the grouping. So four times 15 minus 65 Does that equal Negative. Five. Four times 15 is 60 minus 65. And I'm working my way down and I do get negative. Five is my eyes A true stating equals negative five is a true statement of my solution
The first thing we're doing across most voice or three times five K one secret six times three K minus two were to distribute the three to get 15 K plus three Sikora, distribute the 6 18 K minus 12. When I subtract the 15 k it would get three equals three K minus 12 12 and get 15 equals three K two sulphur care when you just divide by three and we get K equals but
For this one. We have to square, but starts which will give us case squared quota. What we have underneath there out of co over here. All right, so we subtract the case squared, which means that they can still out. So we're left with zero if he could. A negative five K minus 15. All right. When we add, the 15 were left with 15. If you quote to negative five k, we divide by negative five and we get K is equal to negative three. Now we always gonna plug back into our initial equation. When we plug negative three into our initial equation, we get negative. Three is equal to negative. Three squared. It's nine. Very still. We have nine negative. Five times a negative. Three is positive. 15. So we have nine plus 15 which were given 24. 24 Monets, 15. It's nine. A group of nine. This positive three. So this does not work out the business about the Amster and we have no solution to this problem