Divide and Simplify:
y^2-25/7 divided by 7y+35/49
To divide and simplify the expression (y^2 - 25/7) divided by (7y + 35/49), you can follow these steps:
Step 1: Invert the divisor
To divide two fractions, we invert the second fraction and change the division operation to multiplication. Therefore, we rewrite the expression as:
(y^2 - 25/7) multiplied by (49/7y + 35)
Step 2: Simplify
Now, let's simplify further by factoring and canceling out common factors.
First, let's simplify the expression in the numerator by factoring the difference of squares.
The numerator (y^2 - 25) is a difference of squares, which can be factored as (y - 5)(y + 5).
Next, let's simplify the expression in the denominator by factoring out the GCF (Greatest Common Factor).
The denominator (49/7y + 35) has a common factor of 7. We can rewrite it as (7(7/y + 5)).
Now, our expression becomes:
[(y - 5)(y + 5)] multiplied by [49/7(7/y + 5)]
Step 3: Simplify further
Let's cancel out common factors between the numerator and denominator.
The factors (y + 5) cancel out:
[(y - 5)] multiplied by [49/7(7/y)]
Simplified further, we have:
[(y - 5) * 49]/[7 * (7/y)]
Step 4: Simplify the expression
To simplify further, multiply the numerators and denominators:
(49(y - 5))/[(7 * 7)/y]
Simplifying further, we can multiply the fraction by the reciprocal of the denominator to turn the division operation into multiplication:
(49(y - 5)) * (y/(7 * 7))
Finally, simplify the expression:
(49y(y - 5))/(49)
The final simplified expression is:
y(y - 5)