can anyone solve (5 / x) + (3 / x-4) = 4?

(5 / X) + (3 / X-4) = 4

Multiplying both sides with "( X ) . (X - 4)", we have,

5 (X - 4) + 3 (X) = 4 (X).(X - 4)

5X - 20 + 3X = 4X² - 16X

=>

4X² - 16X - 5X - 3X + 20 = 0

4X² - 24X + 20 = 0

4(X² - 6X + 5) = 0

X² - 6X + 5 = 0/4

X² - 6X + 5 = 0

By Factorization, we have

X² - 5X - 1X + 5 = 0

(X² - 5X) - (X - 5) = 0

X(X - 5) - 1(X - 5) = 0

(X - 1) . (X - 5) = 0

=>

X - 1 = 0 ---------- (1)

or

X - 5 = 0 ---------- (2)

By solving Equation 1 & 2, we have

X = 1 & 5

So,

Solution Set = {1 , 5} Ans.

5/x + 3/(x - 4) = 4
5x - 20 + 3x = 4(x² - 4x)
8x - 20 = 4x² - 16x
4x² - 24x = - 20
x² - 3x = - 5 + (- 3)²
x² - 3x = - 5 + 9
(x - 3)² = 4
x - 3 = ± 2

x = 2 + 3, x = 5
x = - 2 + 3, x = 1

Answer: x = 5, 1

Proof (x = 5):
5/5 + 3/(5 - 4) = 4
1 + 3/1 = 4
1 + 3 = 4

Proof (x = 1):
5/1 + 3/(1 - 4) = 4
5 + 3/- 3 = 4
5 - 1 = 4

X =9 is the respond! merely replace each and each of your given 4 solutions in the equation. x=a million, provides you with 3-5 which isn't equivalent to 4. comparable for x=4. Now put in x =9 , and u have 3 x 3 -5 = 4. attempt x=25 and you're way extra beneficial than 4. desire that enables! Cheers

I assume that you mean (5/x) + (3/(x − 4)) = 4

Multiply through by x(x − 4) to clear the fractions

5(x − 4) + 3x = 4x(x − 4)
8x − 20 = 4x² − 16x
4x² − 24x + 20 = 0
x² − 6x + 5 = (x − 5)(x − 1) = 0

x = 1, 5, both of whichwork in the original equation.

5/x + 3/(x - 4) = 4
x(x - 4)[5/x + 3/(x - 4)] = x(x - 4)(4)
5(x - 4) + 3(x) = 4x(x - 4)
5x - 20 + 3x = 4x^2 - 16x
8x - 20 = 4x^2 - 16x
4(2x - 5) = 4(x^2 - 4x)
x^2 - 4x - 2x + 5 = 0
x^2 - 6x + 5 = 0
x^2 - x - 5x + 5 = 0
(x^2 - x) - (5x - 5) = 0
x(x - 1) - 5(x - 1) = 0
(x - 1)(x - 5) = 0

x - 1 = 0
x = 1

x - 5 = 0
x = 5

∴ x = 1, 5

Should be shown as :-

5 / x + 3 / ( x - 4 ) = 4

5 ( x - 4 ) + 3x = 4 x ( x - 4 )

5x - 20 + 3x = 4x^2 - 16 x

4x^2 - 24x + 20 = 0

x^2 - 6x + 5 = 0

( x - 5 ) ( x - 1 ) = 0

x = 1 , x = 5

x=5

(5/5)+(3/5-4)=4
(1)+(3/1)+4
1+3=4

5/x + 3/x =8
5+3=8x
x=1

(5 / x) + (3 / x-4) = 4
(5x -20 + 3x)/(x^2 - 4x) = 4
4x^2 - 16x = 8x - 20
x^2 - 6x + 5 = 0
(x - 5)(x - 1) = 0
x = 5, 1