Solve x ^ 2 + (a/(a + b) + (a + b)/a) * x + 1 = 0

Question

Solve the equation

Solve for x

Solve for a

Solve for b

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

Evaluate

x^{2} + (\frac{a}{a + b} + \frac{a + b}{a}) x + 1 = 0

Simplify

More Steps

x^{2} + \frac{x ( 2 a ^{2} + 2 ab + b ^{2} )}{a ( a + b )} + 1 = 0

Rewrite the expression

x^{2} + \frac{( 2 a ^{2} + 2 ab + b ^{2} ) x}{a ^{2} + ab} + 1 = 0

Multiply both sides of the equation by LCD

(x^{2} + \frac{( 2 a ^{2} + 2 ab + b ^{2} ) x}{a ^{2} + ab} + 1) (a^{2} + ab) = 0 \times (a^{2} + ab)

Simplify the equation

More Steps

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

Any expression multiplied by 0 equals 0

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

Expand the expression

More Steps

a^{2} x^{2} + ab x^{2} + 2 a^{2} x + 2 ab x + b^{2} x + a^{2} + ab = 0

Factor the expression

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(a x + a + b x) (a x + a + b) = 0

When the product of factors equals 0,at least one factor is 0

a x + a + b x = 0 a x + a + b = 0

Solve the equation for x

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x = - \frac{a}{a + b} a x + a + b = 0

Solution

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

Show Solution