Help with these please?!
Simplify the complex expression:
-3
---
5
- + y
x
and
2
-- + 2
x+4
----------
3
-- + 1
x+4
I cannot decipher what you meant to type. Try using parentheses instead of changing to a new line for fractions.
-3/[(5/x)+y]
(2/x+4)+2 over [3/(x+4)]+1
To simplify these complex expressions, we need to start by simplifying the fractions and then simplifying the overall expressions.
For the first expression:
-3/[(5/x)+y]
To simplify the fraction within the square brackets, we need to find a common denominator between 5/x and y. The common denominator in this case is x.
So, we can rewrite the expression as:
-3/[(5/x)+(yx/x)]
Now, we can simplify the expression:
-3/[(5yx + x)/(x * x)]
To divide by a fraction, we can multiply by the reciprocal of that fraction. Thus, we can rewrite the expression as:
-3 * (x * x)/(5yx + x)
This can be further simplified by canceling out any common factors. In this case, the x's cancel out:
-3 * x/(5yx + x)
So, the simplified form of the expression is:
-3x/(5yx + x)
Now, let's move on to the second expression:
(2/x+4) + 2 / [3/(x+4) + 1]
Again, we need to simplify the fractions in the square brackets first.
The expression can be written as:
[(2/x+4) + 2] / [(3/(x+4)) + 1]
The first fraction can be simplified by finding a common denominator between x and 4, which is 4x.
So it becomes:
[(2+4x)/4x]
For the second fraction, we need to find a common denominator between (x+4) and 1, which is (x+4).
So it becomes:
[(3+1(x+4))/(x+4)]
Now we can simplify this expression as:
(2+4x)/4x divided by (3+(x+4))/(x+4)
To divide by a fraction, we can multiply by its reciprocal.
So it becomes:
(2+4x)/4x * (x+4)/(3+(x+4))
Now, we can simplify this expression by canceling out any common factors.
We notice that (2+4x) and (x+4) have a common factor of 2, so we can divide both numerator and denominator by 2.
Similarly, (x+4) and (3+(x+4)) have a common factor of (x+4), so we can divide both numerator and denominator by (x+4).
The expression simplifies to:
(1+2x)/(2x) * 1/3
Multiplying the fractions together:
(1+2x)/(6x)
So, the simplified form of the expression is:
(1+2x)/(6x)