Question #8e9bf

2 Answers
Jul 29, 2017

a=-3\pm\sqrt{35}

Explanation:

Assuming your question says a/2-6/(a-2)=(6-3a)/(a-2)

Steps

  • First move all values with denominator a-2 to the right side.
    a/2=6/(a-2)+(6-3a)/(a-2) Simplify this.
    a/2=(6+6-3a)/(a-2) → Simplify again → a/2=(12-3a)/(a-2)
  • Now find the common denominator to make the fractions equivalent.
    (a(a-2))/(2(a-2))=(2(12-3a))/(2(a-2)) Simplify this.
    (a^2-2)/(2a-4)=(24-6a)/(2a-4) We can now take out the denominator as both sides are equivalent.
  • Calculate to find a: first, set up quadratic. Make one side 0.
    a^2-2=24-6a
    a^2-26+6a=0 reorder this
    a^2+6a-26=0
  • Solving the quadratic here

Answer
a=-3\pm\sqrt{35}

Jul 30, 2017

a=2(2\pm\sqrt{7})

Explanation:

Assuming your question says a/2-6/(a-2)=6-(3a)/(a-2)

Steps

  • First set all denominators equal; common denominator is 2(a-2)
    \therefore\(a(a-2))/(2(a-2))-(2(6))/(a(a-2))=(6(2(a-2)))/(2(a-2))-(2(3a))/(2(a-2))
    simplifying (a^2-2a)/(2a-4)-12/(2a-4)=(12a-24)/(2a-4)-(6a)/(2a-4)
  • Now take out the denominator since everything is equivalent...
    (a^2-2a)-12=(12a-24)-6a
    a^2-2a-12=6a-24 adding like terms on right side...
  • Make a quadratic (form ax^2+bx+c) to solve:
    a^2-8a-12=0 moving all terms to left side...
    solving here

Answer
a=2(2\pm\sqrt{7})