Pick Method on simplifying complex fractions and apply it to

Pick Method on simplifying complex fractions and apply it to the following complex fraction showing all steps.  Reduce your answer to lowest terms.

  

Solution

The problem given is

(X – (14/X-5)) / (2 – (4/X-5))

Step 1: Make the numerator one fraction

i.e. (X(X-5) -14) / (X – 5)

= (X^2 – 5X -14) / (X – 5)

Step 2: Make denominator one fraction

i.e. (2(X – 5) – 4) / (X – 5)

= (2X – 14) / (X – 5)

Step 3: Write the complex fraction with numerator and denominator

i.e. ((X^2 – 5X -14) / (X – 5)) / ((2X – 14) / (X – 5))

Step 4: Invert the denominator and write it as multiplication

((X^2 – 5X -14) * (X - 5)) / (((X – 5) * (2(X – 7)))

Step 5: (X-5) in numerator and denominator gets cancelled and fraction will be

(( X^2 – 5X -14)) / ((2 (X – 7))

Step 6: Factorising Quadratic equation

((X – 7) (X + 2)) / ((2 (X – 7))

Step 7: X-7 in numerator and denominator gets cancelled.

The Answer is

(X+2) / 2