Question

Solving rational equations ???

Answer 1

1.(1/6x2 ) = ( 1/3x2) - (1/x)

2. (1/n2) + (1/n) = (1/2n2)

3. (1/x) = (6/3x) + 1

4. (1/6x2) = (1/2x) + (7/ 6x2)

5. (1/6b2) + (1/6b) = (1/b2)

Answer 2

find common denominators

Answer 3

for example, i would multiply the first equation by 6x^2, giving me

1 = 2 - 6x

x= 1/6

Answer 4

Ok Can you chec the 2nd one for me as i try?

Answer 5

@robz8

Answer 6

1 = 2n +2

n = -1/2

Answer 7

No i wanted to try it and you check it

Answer 8

try it, if you didn't get that answer then you did something wrong

Answer 9

for these problems, you could pick out the "biggest denominator"
and multiply both sides of the equation (all terms) by it.

For example, for
\[ \frac{1}{6x^2 } = \frac{1}{3x^2} - \frac{1}{x}\ \]
\( 6x^2\) is the biggest denominator. if we multiply every term by it we get
\[ 6x^2 \cdot \frac{1}{6x^2 } = 6x^2 \cdot\frac{1}{3x^2} - 6x^2 \cdot\frac{1}{x} \]
or
\[ \frac{6x^2}{6x^2 } = \frac{6x^2}{3x^2} - \frac{6x^2}{x}\ \]
now simplify. of course 6x^2/ 6x^2 is 1
we get
\[ 1 = 2 - 6x\]
do you see how?
now add -2 both sides
\[ 1 + -2 = 2+ -2 - 6x \]
simplify
\[ -1 = -6x \]
divide both sides by -6 to get the answer
\[ \frac{1}{6}=x \]

Answer 10

@phi thanks!