Find all values of $c$ such that $\dfrac{c}{c-5} = \dfrac{4}{c-4}$. If you find more than one solution, then list the solutions you find separated by commas.
Solve for c:
c/(c - 5) = 4/(c - 4)
Multiply both sides by a polynomial to clear fractions.
Cross multiply:
c (c - 4) = 4 (c - 5)
Write the quadratic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
c^2 - 4 c = 4 (c - 5)
Write the linear polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
c^2 - 4 c = 4 c - 20
Move everything to the left hand side.
Subtract 4 c - 20 from both sides:
c^2 - 8 c + 20 = 0
Solve the quadratic equation by completing the square.
Subtract 20 from both sides:
c^2 - 8 c = -20
Take one half of the coefficient of c and square it, then add it to both sides.
Add 16 to both sides:
c^2 - 8 c + 16 = -4
Factor the left hand side.
Write the left hand side as a square:
(c - 4)^2 = -4
Eliminate the exponent on the left hand side.
Take the square root of both sides:
c - 4 = 2 i or c - 4 = -2 i
Look at the first equation: Solve for c.
Add 4 to both sides:
c = 4 + 2 i or c - 4 = -2 i
Look at the second equation: Solve for c.
Add 4 to both sides:
c = 4 + 2 i or c = 4 - 2 i
+36915 c/(c-5) = 4/(c-4) cross multiply to get
c^2 - 4c = 4c-20 simplify to get
c^2 -8c + 20 = 0 Use Quadratic Equation
c = 4 +- sqrt (-16)/2
c= 4+- 2i
