Can someone slove these for me
1.(4x-12)/4x
2.(d+7)/(d^2-49 )
3.(t^2-25)/(t^2+t-20)
4.(2x^2+6x+4)/(4x^2-12x-16)
5.(6-y)/*y^2-2y-24)
all you have to do is reduce like #1
4x-12
______
4x
cross out the 4x b/c it's on the top and bottom which leaves just -12 on the top
You can't do that!!!
That is like saying (4 + 5)/4 = 5
(4x-12)/(4x)
= 4(x-3)/(4x)
= (x-3)/x
To solve these expressions, let's go through each one step by step.
1. (4x-12)/4x:
To reduce this expression, we can start by factoring out the common factor of 4 in the numerator:
(4(x-3))/4x.
Now, we can cancel out the common factor of 4 between the numerator and the denominator, resulting in:
(x-3)/x.
2. (d+7)/(d^2-49):
To simplify this expression, let's factor the denominator, which is the difference of squares:
(d+7)/[(d+7)(d-7)].
We can cancel out the common factor of (d+7) between the numerator and the denominator, giving us the simplified form:
1/(d-7).
3. (t^2-25)/(t^2+t-20):
To simplify this expression, let's factor the numerator and the denominator separately:
(t+5)(t-5)/(t^2+t-20).
We can see that the numerator and the denominator have a common factor of (t-5), so we can cancel it out:
(t+5)/(t^2+t-20).
4. (2x^2+6x+4)/(4x^2-12x-16):
To simplify this expression, we can start by factoring the numerator and the denominator separately:
(2(x^2+3x+2))/(4(x^2-3x-4)).
Now, let's further factor the quadratic expressions in the numerator and denominator:
(2(x+1)(x+2))/(4(x-4)(x+1)).
We can see that the numerator and the denominator have a common factor of (x+1), so we can cancel it out:
(2(x+2))/(4(x-4)).
Finally, we can simplify by dividing both the numerator and denominator by 2:
(x+2)/(2(x-4)).
5. (6-y)/(y^2-2y-24):
To simplify this expression, let's factor the numerator and the denominator separately:
(6-y)/[(y+4)(y-6)].
We can see that there's a negative sign in the numerator, so we can rewrite it as (-1)(y-6):
(-1)(y-6)/[(y+4)(y-6)].
Now, we see that the numerator and the denominator have a common factor of (y-6), so we can cancel it out:
(-1)/(y+4).
Remember to always be cautious when canceling out terms. Make sure they have a common factor and that it doesn't result in any undefined values or contradictions.