What are the solutions to the equation abx^2=(a-b)^2(x+1) ?

The solutions to the equation abx^2=(a-b)^2(x+1) are x=(a-b)/b ,x=(-a+b)/a ;\quad ab\ne 0

Find the zeros of abx^2=(a-b)^2(x+1)

The zeros of abx^2=(a-b)^2(x+1) are x=(a-b)/b ,x=(-a+b)/a ;\quad ab\ne 0

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ab x^{2} = (a - b)^{2} (x + 1)

x = \frac{a - b}{b}, x = \frac{- a + b}{a}; ab \neq = 0

Solution steps

ab x^{2} = (a - b)^{2} (x + 1)

Expand

(a - b)^{2} (x + 1) : a^{2} x + a^{2} - 2 ab x - 2 ab + b^{2} x + b^{2}

ab x^{2} = a^{2} x + a^{2} - 2 ab x - 2 ab + b^{2} x + b^{2}

Subtract

b^{2} x + b^{2}

from both sides

ab x^{2} - (b^{2} x + b^{2}) = a^{2} x + a^{2} - 2 ab x - 2 ab + b^{2} x + b^{2} - (b^{2} x + b^{2})

Simplify

ab x^{2} - b^{2} x - b^{2} = a^{2} x + a^{2} - 2 ab x - 2 ab

Subtract

- 2 ab x - 2 ab

from both sides

ab x^{2} - b^{2} x - b^{2} - (- 2 ab x - 2 ab) = a^{2} x + a^{2} - 2 ab x - 2 ab - (- 2 ab x - 2 ab)

Simplify

ab x^{2} - b^{2} x - b^{2} + 2 ab x + 2 ab = a^{2} x + a^{2}

Subtract

a^{2} x + a^{2}

from both sides

ab x^{2} - b^{2} x - b^{2} + 2 ab x + 2 ab - (a^{2} x + a^{2}) = a^{2} x + a^{2} - (a^{2} x + a^{2})

Simplify

ab x^{2} + (- b^{2} + 2 ab - a^{2}) x - b^{2} + 2 ab - a^{2} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - b ^{2} + 2 ab - a ^{2} ) \pm ( - b ^{2} + 2 ab - a ^{2} ) ^{2} - 4 ab ( - b ^{2} + 2 ab - a ^{2} )}{2 ab}

Simplify

(- b^{2} + 2 ab - a^{2})^{2} - 4 ab (- b^{2} + 2 ab - a^{2}) : (a + b) (a - b)

x_{1, 2} = \frac{- ( - b ^{2} + 2 ab - a ^{2} ) \pm ( a + b ) ( a - b )}{2 ab}; ab \neq = 0

Separate the solutions

x_{1} = \frac{- ( - b ^{2} + 2 ab - a ^{2} ) + ( a + b ) ( a - b )}{2 ab}, x_{2} = \frac{- ( - b ^{2} + 2 ab - a ^{2} ) - ( a + b ) ( a - b )}{2 ab}

x = \frac{- ( - b ^{2} + 2 ab - a ^{2} ) + ( a + b ) ( a - b )}{2 ab} : \frac{a - b}{b}

x = \frac{- ( - b ^{2} + 2 ab - a ^{2} ) - ( a + b ) ( a - b )}{2 ab} : \frac{- a + b}{a}

The solutions to the quadratic equation are:

x = \frac{a - b}{b}, x = \frac{- a + b}{a}; ab \neq = 0

- 6 x^{2} - 586 = 84 x - 484 x - 4

15 x^{2} + 6 = 2 x

x, x^{2} + 7 x + 12 = 0

0 = x^{2} - 3 x + 3

0 = x^{2} - 3 x + 9

What are the solutions to the equation abx^2=(a-b)^2(x+1) ?
The solutions to the equation abx^2=(a-b)^2(x+1) are x=(a-b)/b ,x=(-a+b)/a ;\quad ab\ne 0
Find the zeros of abx^2=(a-b)^2(x+1)
The zeros of abx^2=(a-b)^2(x+1) are x=(a-b)/b ,x=(-a+b)/a ;\quad ab\ne 0