Solve the equation. (5)/(y-5) - (7)/(4y+9) + (2)/(y-5) =...

Solve the equation. \frac{5}{y-5} - \frac{7}{4y+9} + \frac{2}{y-5} = 0 Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are y = (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. There is no solution.

Transcript

00:01 All right, we need to solve this and we are going to use the quadratic formula, the negative b plus or minus b squared.

00:06 I'm not going to read it all.

00:07 But i'm going to highlight that our a value is a coefficient right here.

00:12 I thought i had my pen up.

00:13 The a value is 3.

00:15 The b value is negative 4 and the c value is negative 2.

00:19 Super important to know that because that's what i'm going to plug in here.

00:22 Excuse me.

00:24 So negative b and negative negative 4 is a positive 4 plus or minus.

00:30 Negative 4 squared is 16 minus 4 times our a value is 3 times our c value of negative all over 2a, which is 2 times 3.

00:47 Alright, i'm going to simplify across.

00:50 So why don't i do one thing here? maybe i'll do it in green.

00:55 16, well, let's do this.

00:56 4 times 3 is 12 and 12 times 2.

01:00 I'll keep the negatives.

01:01 Negative 4 times 3 is negative 12 and a negative 12 times a negative 2 is a positive 24.

01:09 So this whole thing's become 16 plus 24, which is 40 and so that's going to help us save room 4 plus or minus the square root of 40 over 2 times 3 is 6.

01:23 Alright, of course we're going to rewrite 40 to be 4 times 10 because that's going to be more useful for us because because because at this point we've probably seen in the lesson 4 is a square.

01:38 It is 2 squared so i can pull a 2 outside of that radical.

01:41 So now we got 4 plus or minus 2 square root 10.

01:47 And there's nothing else we can pull out a square root 10 because i mean that's 2 times 5.

01:51 No squares there...

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