Question

What is the LCD of `\frac { x + 5} { 4x - 12} - \frac { 2} { x - 3}`?

Answer 1

See solution explanation below:

Explanation:

Multiply the fraction on the right by `color(red)(4/4)`:

`4/4 xx 2/(x - 3) => (color(red)(4) * 2)/(color(red)(4)(x - 3)) => 8/((color(red)(4) * x) - (color(red)(4) * 3)) =>`

`8/(4x - 12)`

Therefore the LCD (Lowest Common Denominator) is: `4x - 12`

and the expression can be rewritten as:

`(x + 5)/(4x - 12) - 8/(4x - 12)`