We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# 1 question

0
232
1

Q1) thank you

Nov 9, 2018

### 1+0 Answers

#1
+1

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