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2/x+2=9/8-5x/4x+8
solve rational equation

User Teun D
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To solve the rational equation 2/(x + 2) = 9/(8 - 5x)/(4x + 8), we first simplify the right side by multiplying the numerator and denominator by the LCD of 4x + 8:

2/(x + 2) = 9(4x + 8)/(8 - 5x)

2/(x + 2) = (36x + 72)/(5x - 8)

Now we can cross-multiply and simplify:

2(5x - 8) = (x + 2)(36x + 72)

10x - 16 = 36x^2 + 80x + 144

36x^2 + 70x + 160 = 0

We can simplify this quadratic equation by dividing both sides by 2:

18x^2 + 35x + 80 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 18, b = 35, and c = 80:

x = (-35 ± sqrt(35^2 - 4(18)(80))) / 2(18)

x = (-35 ± sqrt(137)) / 36

Therefore, the solutions to the rational equation 2/(x + 2) = 9/(8 - 5x)/(4x + 8) are:

x = (-35 + sqrt(137)) / 36
x = (-35 - sqrt(137)) / 36
User Kars
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