You can
put this solution on YOUR website!your equation is:
1/(x-4) + 4/(4x-4) = 5/4
factor out the 4 in 4/(4x-4) to get:
1/(x-4) + 1/(x-1) = 5/4
your common denominator is going to be (x-4)*(x-1)
multiply 1/(x-4) * (x-1)/(x-1) to get (x-1)/((x-4)*(x-1))
multiply 1/(x-1) * (x-4)/(x-4) to get (x-4)/(x-4)*(x-1)))
your equation becomes:
(x-1)/((x-4)*(x-1)) + (x-4)/((x-4)*x-1)) = 5/4
combine the two fractions with the common denominator to get:
((x-1) + (x-4)) / ((x-4)*(x-1)) = 5/4
simplify by combining like terms to get:
(2x-5)/ ((x-4)*(x-1)) = 5/4
multiply both sides of this equation by 4 to get:
(4 * (2x-5))/ ((x-4)*(x-1)) = 5
simplify by removing parentheses in the numerator on the left hand side of the equation to get:
(8x-20) / ((x-4)*(x-1)) = 5
multiply both sides of this equation by ((x-4)*(x-1)) to get:
8x-20 = 5 * ((x-4)*(x-1))
simplify by performing indicated operations and removing parentheses to get:
8x-20 = 5x^2 - 25x + 20
subtract 8x from both sides of the equation and add 20 to both sides of the equation to get:
0 = 5x^2 - 33x + 40 which is the same as:
5x^2 - 33x + 40 = 0
use the quadratic equation to solve this equation to get:
x = 5
or
x = 1.6
substitute for x in the original equation to confirm the result.
I did that and the results are confirmed so these values are your answer.
The quadratic formula is:
the standard form of the quadratic equation is:
ax^2 + bx + c = 0
your equation is:
5x^2 - 33x + 40 = 0
a = 5
b = -33
c = 40
plug those values into the quadratic formula and you get:
which becomes:
which becomes:
The result is x = 5 or x = 1.6
