Question

24/х-4 - 25/х+4=-9 х+2/х - х/х-3=7/50

Answer 1

Разность квадратов,домнож первое 24/х-4 на х+4,а со следующим наоборот и ты избавишься от знаменателя

Answer 2

To solve this system of equations, we'll first simplify each equation and then solve for the variable x. Let's start with the first equation:

1. (24/(x - 4)) - (25/(x + 4)) = -9

To simplify this equation, you can find a common denominator, which is (x - 4)(x + 4):

(24(x + 4) - 25(x - 4))/((x - 4)(x + 4)) = -9

Now, simplify the equation further:

(24x + 96 - 25x + 100)/((x - 4)(x + 4)) = -9

(-x + 196)/((x - 4)(x + 4)) = -9

Next, cross-multiply:

-9(x - 4)(x + 4) = -x + 196

Now, expand and simplify:

-9(x^2 - 16) = -x + 196

-9x^2 + 144 = -x + 196

Now, let's move all the terms to one side of the equation:

-9x^2 + x - 196 + 144 = 0

-9x^2 + x - 52 = 0

Now, let's move on to the second equation:

2. (x + 2)/x - x/(x - 3) = 7/50

To simplify this equation, find a common denominator, which is x(x - 3):

((x + 2)(x - 3)/x(x - 3)) - (x(x - 3)/x(x - 3)) = 7/50

Now, simplify further:

(x^2 - x - 3x - 6 - x^2 + 3x)/x(x - 3) = 7/50

(-6)/x(x - 3) = 7/50

Now, cross-multiply:

-6 * 50 = 7 * x(x - 3)

-300 = 7x^2 - 21x

Now, move all the terms to one side of the equation:

7x^2 - 21x - 300 = 0

Now you have two quadratic equations:

1. -9x^2 + x - 52 = 0
2. 7x^2 - 21x - 300 = 0

You can solve these equations separately. Let's solve the first one:

1. -9x^2 + x - 52 = 0

You can use the quadratic formula for this equation:

x = (-b ± √(b² - 4ac)) / (2a)

For this equation, a = -9, b = 1, and c = -52. Plugging in these values:

x = (-1 ± √(1² - 4(-9)(-52))) / (2(-9))

x = (-1 ± √(1 + 1872)) / (-18)

x = (-1 ± √1873) / (-18)

Now, let's solve the second equation:

2. 7x^2 - 21x - 300 = 0

You can also use the quadratic formula for this equation:

x = (-b ± √(b² - 4ac)) / (2a)

For this equation, a = 7, b = -21, and c = -300. Plugging in these values:

x = (21 ± √((-21)² - 4(7)(-300))) / (2(7))

x = (21 ± √(441 + 8400)) / 14

x = (21 ± √(8841)) / 14

Now you have two sets of possible solutions for x:

1. x = (-1 + √1873) / (-18) and x = (21 + √8841) / 14
2. x = (-1 - √1873) / (-18) and x = (21 - √8841) / 14

You can calculate the approximate values for these solutions.