Question

simplify 1/x-3+4/x / 4/x-1/x-3

Answer 1

\[\frac{\frac{1}{x-3}+\frac{4}{x} }{ \frac{4}{x}-\frac{1}{x-3}}\]\[=\frac{\frac{1(x)}{(x-3)x}+\frac{4(x-3)}{x(x-3)} }{ \frac{4(x-3)}{x(x-3)}-\frac{1(x)}{(x-3)x}}\]\[=\frac{\frac{x+4x-12}{x(x-3)} }{ \frac{4x-12-x}{(x-3)x}}\]\[=\frac{5x-12}{ 3x-12}\]\[=?\]

Answer 2

Numerator 1/x-3 + 4/x = x + 4(x -3) / (x-3)*x
= x + 4x - 3 / (x-3)*x
=5x - 3 / (x -3)*x

denominator 4/x - 1/x-3 = 4(x-3) - x / x*(x-3)
=4x - 12 - x / x(x-3)
=3x - 12 / x(x-3)

dividing we get (the bottom gets cancelled)

5x -3 / 3x-12
=5x - 3 / 3(x-4)

Answer 3

hmmm but thats not one of the options

Answer 4

@sammy90210 Do you know how to do factorization?

Answer 5

no

Answer 6

Do you know what factor is?

Answer 7

to combine

Answer 8

._. what is the common factor of 3x and -12?

Answer 9

3

Answer 10

Yes. when you have the expression 3x-12 and you need to factorise it, take out the common factor 3 and group the rest of terms, ie 3x-12 = 3(x-4)
Now, you've factorised the denominator. Can you get the answer now?

Answer 11

5x-12 / 3(x-4)

Answer 12

Yes :)

Answer 13

thanks callisto!:)

Answer 14

Welcome!