How do you solve $\frac{x - 4}{x - 2} = \frac{x - 2}{x + 2} + \frac{1}{x - 2}$ $(x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)$ ?

Question

How do you solve $\frac{x - 4}{x - 2} = \frac{x - 2}{x + 2} + \frac{1}{x - 2}$ $(x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)$ ?

1 Answer

Related questions

What is Clearing Denominators in Rational Equations?
How do you solve rational expressions by multiplying by the least common multiple?
How do you solve $5 x - \frac{1}{x} = 4$ $5x-\frac{1}{x}=4$ ?
How do you solve $- 3 + \frac{1}{x + 1} = \frac{2}{x}$ $-3 + \frac{1}{x+1}=\frac{2}{x}$ by finding the least common multiple?
What is the least common multiple for $\frac{x}{x - 2} + \frac{x}{x + 3} = \frac{1}{x^{2} + x - 6}$ $\frac{x}{x-2}+\frac{x}{x+3}=\frac{1}{x^2+x-6}$ and how do...
How do you solve $\frac{x}{x^{2} - 36} + \frac{1}{x - 6} = \frac{1}{x + 6}$ $\frac{x}{x^2-36}+\frac{1}{x-6}=\frac{1}{x+6}$ ?
How do you solve by clearing the denominator of $\frac{3}{x} + \frac{2}{x^{2}} = 4$ $3/x+2/x^2=4$ ?
How do you solve $\frac{2}{x^{2} + 2 x + 1} - \frac{3}{x + 1} = 4$ $2/(x^2+2x+1)-3/(x+1)=4$ ?
How do you solve equations with rational expressions $\frac{1}{x} + \frac{2}{x} = 10$ $1/x+2/x=10$ ?
How do you solve for y in $\frac{y + 5}{2} - \frac{y}{3} = 1$ $(y+5)/ 2 - y/3 =1$ ?

Impact of this question

3425 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-24T21:00:20

$x - 4 = \frac{(x - 2) (x - 2)}{x + 2} + 1$ $x-4 = ((x-2)(x-2))/(x+2) + 1$
$(x - 4) (x + 2) = (x - 2) (x - 2) + (x + 2)$ $(x-4)(x+2) = (x-2)(x-2) + (x+2)$
$x^{2} - 2 x - 8 = x^{2} - 4 x + 4 + x + 2$ $x^2 - 2x - 8 = x^2-4x+4 + x + 2$

Simplify
$2 x - 12 = x + 2$ $2x - 12 = x + 2$
$x = 14$ $x = 14$

Explanation:

The easiest way to do this type of calculation is to get rid of all the denominators. To do this, first times every single term by $x - 2$ $x-2$ , then do the same, but with $x + 2$ $x+2$ . At that point, it becomes a matter of simplification.

Science

Math

Humanities

... and beyond

How do you solve $\frac{x - 4}{x - 2} = \frac{x - 2}{x + 2} + \frac{1}{x - 2}$ $(x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve (x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)x−4x−2=x−2x+2+1x−2 (x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $\frac{x - 4}{x - 2} = \frac{x - 2}{x + 2} + \frac{1}{x - 2}$ $(x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)$ ?