Algebra

Question 1

How will you multiply the following?

5/x + 3/x^2

Write it in a paper for easy elaboration

Hint: LCD

Answer 1

The least common denominator for both sides is (x) so we add them at the first fraction

5(x)/x(x)+3/x^2

hence our equation will turn into

5x/x2+3/x2

Now our denominator are similar
We can rationalize it as

5x+3/x2

Question 2

Rationalize the following

x-3/4 - x+2/3

Answer 2

Add the denominator or the first fraction to both sides of the second denominator and vise versa

(3) x-3 x+2 (4)
———— - —————
(3) 4 3 (4)

Distribute them

3x-9 4x+8
———— - —————
12 12

3x - 9 - (4x + 8)
————————
12

now we can rationalize them as

-x - 17 -1(x-17)
———— or ————
12 12

Question 3

How do you add two dissimilar terms?

Answer 3

Write them both as term A + Term B

Question 4

What is the quadratic formula?

Answer 4

x = -b + or - [Square root of] b^2 - 4ac/ 2a

Question 5

Solve for k

6/(2k -6) = 3

Answer 5

HINT: Multiply both sides that will remove the quotient

Step 1 Multiply both sides with the quotient

Step 2 Cancel both (2k - 6)

Step 3 Multiply 3 to (2k - 6) in the other side of the equation

Step 4 Now you’ll get 6 = 6k - 18

Step 5 Get the reciprocal of the equation and bring the 18 to the left side of the equation. It will turn into 6 + 18 = 6k or 24 = 6k

Step 6 Divide both sides with 6 and you’ll get 4 = k

Therefore k = 4 :>

Question 6

Solve for x

x + 1 / 9 - x = 2/3

Answer 6

HINT: Everything you needs is either in the equation already or the reciprocal of a term or a fraction

Step 1. Multiply both sides by 9 - x to remove the quotient

Step 2. Multiply 2/3 to 9 - x, you’ll get 6 - 2/3x

Step 3. To be able to distribute the fraction from the right term, the left term must have a fraction too. So take the “x” which has a “1” and make it into a useful fraction. In this scenario it’ll be 3/3

Step 4. Now go ahead and distribute 2/3x to the left side of the equation.

Step 5. 3/3 • 2/3 = 3+2/3 so you’ll get 5/3

Step 6. Our equation is now 5/3x + 1 = 6, now to remove the “+1” divide both sides with “-1”

Step 7. 5/3x = 5, now get the reciprocal of the fraction in the left term which is 3/5 and multiply it to both sides. This will eliminate the fraction isolating the x and the remaining “5” will be cancelled from the added equation.

So the answer is x = 3 :,» (I swear math will kill my braincells) jk