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Solving a Quadratic Equation by Completion of Squares Method

Solve: x/a-a+...

Question

Solve: $\frac{x}{a} - \frac{a + b}{x} = \frac{b (a + b)}{a x} .$

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Solution

$x over a minus fraction numerator a plus b over denominator x end fraction equals fraction numerator b left parenthesis a plus b right parenthesis over denominator a x end fraction fraction numerator x squared minus a squared minus a b over denominator a x end fraction equals fraction numerator a b plus b squared over denominator a x end fraction x squared minus a squared minus a b equals a b plus b squared x squared equals a squared plus b squared plus 2 a b x squared equals left parenthesis a plus b right parenthesis squared x equals a plus b$

or x= -(a+b)

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Similar questions

\frac{x}{a} - \frac{a + b}{x} = \frac{b (a + b)}{a x}

x

\frac{x}{a} - \frac{a + b}{x} = \frac{b (a + b)}{a x}

Q. Solve the equation

\frac{(x - b) (x - c)}{(a - b) (a - c)} + \frac{(x - c) (x - a)}{(b - c) (b - a)} + \frac{(x - a) (x - b)}{(c - a) (c - b)} = 1.

Q. Solve the following quadratic equations by factorization:

\frac{x - a}{x - b} + \frac{x - b}{x - a} = \frac{a}{b} + \frac{b}{a}

x = \frac{2 a b}{a + b}

then find the value of

\frac{x + a}{x - a} + \frac{a + b}{a - b}

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Solving a Quadratic Equation by Completion of Squares Method

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