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Q1)

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 Nov 9, 2018
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Solve for j:
(j + 4)/(j + 2) = 2 - 1/j

Write the right hand side as a single fraction.
Bring 2 - 1/j together using the common denominator j:
(j + 4)/(j + 2) = (2 j - 1)/j

Multiply both sides by a polynomial to clear fractions.
Cross multiply:
j (j + 4) = (j + 2) (2 j - 1)

Write the quadratic polynomial on the left hand side in standard form.
Expand out terms of the left-hand side:
j^2 + 4 j = (j + 2) (2 j - 1)

Write the quadratic polynomial on the right-hand side in standard form.
Expand out terms of the right-hand side:
j^2 + 4 j = 2 j^2 + 3 j - 2

Move everything to the left-hand side.
Subtract 2 j^2 + 3 j - 2 from both sides:
-j^2 + j + 2 = 0

Factor the left hand side.
The left-hand side factors into a product with three terms:
-(j - 2) (j + 1) = 0

Multiply both sides by a constant to simplify the equation.
Multiply both sides by -1:
(j - 2) (j + 1) = 0

Find the roots of each term in the product separately.
Split into two equations:
j - 2 = 0 or j + 1 = 0

Look at the first equation: Solve for j.
Add 2 to both sides:
j = 2 or j + 1 = 0

Look at the second equation: Solve for j.
Subtract 1 from both sides:

j = 2    or    j = -1

 Nov 9, 2018

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