Solve f-f1/c-c1 = f^2-f1/c^2-c1

Question

Solve the equation

Solve for c

Solve for f

c = \frac{1 + - 3 + 4 f}{2 - 2 f} c = \frac{1 - - 3 + 4 f}{2 - 2 f}

Evaluate

f - f \times \frac{1}{c} - c \times 1 = f^{2} - f \times \frac{1}{c ^{2}} - c \times 1

Cancel equal terms on both sides of the expression

f - f \times \frac{1}{c} = f^{2} - f \times \frac{1}{c ^{2}}

Multiply the terms

f - \frac{f}{c} = f^{2} - f \times \frac{1}{c ^{2}}

Multiply the terms

f - \frac{f}{c} = f^{2} - \frac{f}{c ^{2}}

Multiply both sides of the equation by LCD

(f - \frac{f}{c}) c^{2} = (f^{2} - \frac{f}{c ^{2}}) c^{2}

Simplify the equation

More Steps

f c^{2} - f c = (f^{2} - \frac{f}{c ^{2}}) c^{2}

Simplify the equation

More Steps

f c^{2} - f c = f^{2} c^{2} - f

Move the expression to the left side

f c^{2} - f c - (f^{2} c^{2} - f) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

f c^{2} - f c - f^{2} c^{2} + f = 0

Collect like terms by calculating the sum or difference of their coefficients

(f - f^{2}) c^{2} - f c + f = 0

Substitute a= f - f^{2},b= - f and c= f into the quadratic formula c = \frac{- b \pm b ^{2} - 4 a c}{2 a}

c = \frac{f \pm ( - f ) ^{2} - 4 ( f - f ^{2} ) f}{2 ( f - f ^{2} )}

Simplify the expression

c = \frac{f \pm ( - f ) ^{2} - 4 ( f - f ^{2} ) f}{2 f - 2 f ^{2}}

Simplify the expression

More Steps

c = \frac{f \pm - 3 f ^{2} + 4 f ^{3}}{2 f - 2 f ^{2}}

Simplify the radical expression

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c = \frac{f \pm f - 3 + 4 f}{2 f - 2 f ^{2}}

Separate the equation into 2 possible cases

c = \frac{f + f - 3 + 4 f}{2 f - 2 f ^{2}} c = \frac{f - f - 3 + 4 f}{2 f - 2 f ^{2}}

Simplify the expression

More Steps

c = \frac{1 + - 3 + 4 f}{2 - 2 f} c = \frac{f - f - 3 + 4 f}{2 f - 2 f ^{2}}

Solution

More Steps

c = \frac{1 + - 3 + 4 f}{2 - 2 f} c = \frac{1 - - 3 + 4 f}{2 - 2 f}

Show Solution