3/y+2 over 7/y-4 can u please show me the steps on how you got the answer. Thank You
3/(y+2) / (7/y-4))
= 3/(y+2) * (y-4)/7
= (3y-12)/(7y+14) or
3(y-4)/[7(y+2)]
To simplify the expression (3/y+2) / (7/y-4), we need to find a common denominator for both fractions.
Step 1: Multiply the numerator and denominator of the first fraction (3/y+2) by (y-4). This gives us (3(y-4)) / ((y+2)(y-4)).
Step 2: Multiply the numerator and denominator of the second fraction (7/y-4) by (y+2). This gives us (7(y+2)) / ((y-4)(y+2)).
Now, our expression becomes (3(y-4)) / ((y+2)(y-4)) divided by (7(y+2)) / ((y-4)(y+2)).
Step 3: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of (7(y+2)) / ((y-4)(y+2)) is ((y-4)(y+2)) / (7(y+2)).
So, our expression simplifies to (3(y-4)) / ((y+2)(y-4)) * ((y-4)(y+2)) / (7(y+2)).
Step 4: Simplify the expression by canceling out common factors. The (y-4) factor in the numerator and denominator cancels out, as well as (y+2) factor.
After canceling out the common factors, our expression becomes 3 / 7.
Therefore, the simplified form of the given expression is 3/7.
To simplify the expression (3/y+2) / (7/y-4), we can follow these steps:
Step 1: Simplify the individual fractions within the expression.
- The numerator 3/y+2 can be simplified by factoring out the common factor of y. This gives us 3/(y*(y/3) + 2).
- The denominator 7/y-4 can be simplified by factoring out the common factor of y. This gives us 7/(y*(7/y) - 4).
Step 2: Simplify the expression.
- Simplify the numerator: y*(y/3) + 2 = (y^2/3) + 2
- Simplify the denominator: y*(7/y) - 4 = 7 - 4 = 3
Step 3: Rewrite the expression using the simplified forms.
- The expression becomes (3/((y^2/3) + 2)) / (7/3).
Step 4: Multiply by the reciprocal of the denominator (7/3).
- This is equivalent to multiplying by 3/7.
Step 5: Simplify the expression further.
- Multiply the numerators: 3 * 3 = 9.
- Multiply the denominators: (y^2/3) + 2 * 7/3 = (7y^2 + 14)/3.
Step 6: Write the final simplified expression.
- The expression simplifies to 9 / ((7y^2 + 14)/3).
Note: It is important to keep in mind the order of operations (PEMDAS/BODMAS) when simplifying the expression.