Simplify [1+y/(x+y)]/ [1-3y2/(x2-y2)]
a.x/y-x
b.y/x-y
c.x-y/2-2x
d.x-y/x-2y
1 + 7/(x+y) = (x+2y)/(x+y)
1 - 3y^2/(x^2-y^2) = (x^2-4y^2)/(x^2-y^2)
so, the result is
(x+2y)/(x+y) * (x+y)(x-y) / (x-2y)(x+2y) = (x-y)/(x-2y)
i get the answer but ,,still i wonder how you get that equation ,, when i try to solve it,this is the output
(1+y/x+y)/(x^2-y^2/1-3y^2).can you explain it to me further?how u get that equation above?
tnx mr. steve
Huh? I clearly showed the factors of each polynomial. When you divide by a fraction, it is the same as multiplying by its reciprocal.
If you can't follow those steps, I fear you have a long road ahead...
Sorry about the typo. 7 is near the y on the keyboard. I meant
1 + y/(x+y) = (x+2y)/(x+y)
Suppose you had
1 + 3/8
you put everything over a common denominator if 8, so you have
8/8 + 3/8 = (8+3)/8
1 + y/(x+y) is done the same way
(x+y)/(x+y) + y/(x+y)
(x+y+y)/(x+y)
(x+2y)/(x+y)
To simplify the expression [1+y/(x+y)]/ [1-3y^2/(x^2-y^2)], we can follow these steps:
Step 1: Simplify the numerator.
In the numerator, we have 1+y/(x+y). To simplify this, we need to find a common denominator for y/(x+y). The common denominator is (x+y). So, we can rewrite 1+y/(x+y) as [(x+y)/(x+y)] + y/(x+y). This simplifies to (x+y+y)/(x+y) which further simplifies to (x+2y)/(x+y).
Step 2: Simplify the denominator.
In the denominator, we have 1-3y^2/(x^2-y^2). To simplify this, we need to factor the denominator. The denominator can be written as (1-3y^2)/[(x+y)(x-y)].
Step 3: Simplify the overall expression.
Now, we can substitute the simplified numerator and denominator back into the original expression. The expression becomes [(x+2y)/(x+y)] / [(1-3y^2)/[(x+y)(x-y)]].
To divide by a fraction, we can multiply by the reciprocal of the fraction. So, we can rewrite the expression as [(x+2y)/(x+y)] * [(x+y)(x-y)/(1-3y^2)].
Next, we can cancel out common factors between the numerator and the denominator. The (x+y) terms will cancel out from the numerator and denominator, leaving us with (x+2y) * (x-y) / (1-3y^2).
Finally, we can expand the numerator and simplify the expression further:
(x^2 - y^2 + 2xy - 2y^2) / (1 - 3y^2).
Based on the simplification steps, the simplified expression is:
(x^2 - y^2 + 2xy - 2y^2) / (1 - 3y^2).
None of the provided answer choices (a, b, c, d) match this simplified expression.