How do you simplify this algebra equation?

x+3/(x-4) divided by 3+x/(x-4)

..........3
x + -----------
.......(x - 4)
-----------------
..........x
3 + -----------
.......(x - 4)


.......x(x - 4) + 3
.......-----------------
...........(x - 4)
= ------------------------
.......3(x - 4) + x
.......----------------
...........(x - 4)


.......x^2 - 4x + 3
.......-----------------
...........(x - 4)
= ------------------------
........3x - 12 + x
.......----------------
...........(x - 4)




.......x^2 - 4x + 3
.......-----------------
...........(x - 4)
= ------------------------
...........4x - 12
.......----------------
...........(x - 4)


.......(x - 1)(x - 3)
.......-----------------
...........(x - 4)
= ------------------------
..........4(x - 3)
.......----------------
...........(x - 4)



.......(x - 1)(x - 3)......(x - 4)
= ....----------------- * ---------------
...........(x - 4)..........4(x - 3)


The factors (x - 3) and (x - 4) cancel out:

........(x - 1)
= ....----------
...........4


Answer: (x - 1) / 4

= ([x + 3]/[x - 4])/([3 + x]/[x - 4])
= ([x + 3]/[x - 4])([x - 4]/[3 + x])
= 1

Answer: 1—the numerators and the denominators of the dividend and the divisor cancel out each other.

(x + 3)/(x - 4) ÷ (3 + x)/(x - 4)
= (x + 3)/(x - 4) * (x - 4)/(x + 3)
= [(x + 3) * (x - 4)]/[(x - 4) * (x + 3)]
= 1

Interpretation of your expression as (x+3)/(x-4) divided by (3+x)/(x-4) is wrong ( which will equal 1). The expression is rightly
x+[3/(x-4)] divided by 3+[x/(x-4)] which works out to be
(x^2-4x+3)/(x-4) divided by (4x-12)/(x-4)
which is (x-3)(x-1)/(x-4) divided by 4(x-3)/(x-4)
which is (x-1)/4

(x+3)/(x-4){(3+x)/(x-4)

To divide by a fraction,flip the fraction and multiply.
(x+3)/(x-4)*(x-4)/(3+x)

Reorder the polynomial 3+x alphabetically from left to right,starting with the highest order term.
(x+3)/(x-4)*(x-4)/(x+3)

Cancel the common factor of (x-4) from the denominator of the first expression and the numerator of the second expression.
(x+3)/(<X>(x-4)<x>)*(<X>(x-4)<x>)/(x+3)

Cancel the common factor of (x-4) from the denominator of the first expression and the numerator of the second expression.
(x+3)*1/(x+3)

Multiply the rational expressions to get ((x+3))/((x+3) ).
(x+3)/(x+3)

Reduce the expression by canceling out the common factor of (x+3) from the numerator and denominator.
(<X>(x+3)<x>)/(<X>(x+3)<x>)

Reduce the expression by canceling out the common factor of (x+3) from the numerator and denominator.
1

(x+3)/(x-4) / (x+3)/(x-4)=1
=============================
far X far / near X near,they used to call it when I was a 5th grader
in 1960's

x+3/(x-4) divided by 3+x/(x-4)
=x+3/x-4 Multiplied by x-4/3+x (eg. 1 divided by 2/3 = 1 multiplied 3/2)
=1

Answer is 1.

well x+3/(x-4)divided by 3+x/(x-4) is equal to x+3/(x-4) times (x-4)/x+3.
So now you can cross out the (x-4)'s and the (3+x)'s, which would leave you with one.

x+3 all over x-4 divided by x+3 all over x-4.
x+3 all over x-4 time x-4 all over x+3
The answer is 1 because of cancelling.