express (1/x-2)-(2/x+5)=(3/x+1) in the form of ax^2+bx=0
hey can u please expand it and symplify coz am stack plz help i dnt knw it, just show me and get the answer
I suspect you are looking at
1/(x-2) - 2/(x+5) = 3/(x+1)
The LCD is (x-2)(x+5)(x+1) , so multiply each term by that to get
(x+5)(x+1) - 2(x-2)(x+1) = 3(x+5)(x-2)
now, carefully expand this, collect all like terms and express the
equation if the required form.
To express the equation (1/x-2)-(2/x+5)=(3/x+1) in the form of ax^2 + bx = 0, let's first simplify the equation:
(1/x - 2) - (2/x + 5) = (3/x + 1)
To combine like terms, we need to find a common denominator for all three fractions. The common denominator in this case is (x)(x + 5)(x + 1):
[(x + 5) - 2(x + 1)](x)(x + 5)(x + 1) = (3)(x)(x + 1)
Now, let's simplify the equation further:
(x + 5 - 2x - 2)(x)(x + 5)(x + 1) = 3x(x + 1)
Simplifying the left side of the equation gives us:
(-x + 3)(x)(x + 5)(x + 1) = 3x(x + 1)
Expanding both sides of the equation gives us:
(-x^2 - 5x + 3x + 15)(x^2 + 6x + 5) = 3x^2 + 3x
Simplifying the left side of the equation gives us:
(-x^2 - 2x + 15)(x^2 + 6x + 5) = 3x^2 + 3x
Now, let's expand and simplify both sides:
(-x^4 - 2x^3 + 15x^2 + 6x^3 + 12x^2 + 90x + 5x^2 + 10x + 75) = 3x^2 + 3x
Combining like terms gives us:
-x^4 + 4x^3 + 22x^2 + 100x + 75 = 3x^2 + 3x
Rearranging the equation:
x^4 - 4x^3 - 19x^2 - 97x - 75 = 0
Therefore, the equation (1/x-2)-(2/x+5)=(3/x+1) expressed in the form of ax^2 + bx = 0 is x^4 - 4x^3 - 19x^2 - 97x - 75 = 0.