1/x = 5/x-2 - 4 /x-3 1/x - 2x/ x+1 =0 2y-5 / y+5 = 3y+21/2y-1

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вопрос

To solve the equations:

1/x = 5/(x-2) - 4/(x-3)
To find a common denominator, multiply each term by (x)(x-2)(x-3):
x(x-2)(x-3)(1/x) = x(x-2)(x-3)(5/(x-2)) - x(x-2)(x-3)(4/(x-3))
(x-3) = 5x(x-3) - 4x(x-2)
(x-3) = 5x^2 - 15x - 4x^2 + 8x
x - 3 = x^2 - 7x
x^2 - 8x + 3 = 0
This equation is a quadratic equation that can be solved using the quadratic formula.

1/x - 2x/(x+1) = 0
Multiply through by x(x+1) to remove the fractions:
(x+1) - 2x^2 = 0
Expand and simplify:
x + 1 - 2x^2 = 0
-2x^2 + x + 1 = 0
This equation is also a quadratic equation that can be solved using the quadratic formula.

(2y-5)/(y+5) = (3y+21)/(2y-1)
Cross multiply:
2y-5 * (2y-1) = (y+5)(3y+21)
Expand and simplify:
2(2y^2 - y - 5) = (y+5)(3(y+7))
4y^2 - 2y - 10 = 3y^2 + 21y + 15
Subtract everything to one side:
y^2 + 23y + 25 = 0
This equation is also a quadratic equation that can be solved using the quadratic formula.