1.4x12 / 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

1. 12 [4x] cancels out. so you're left with just 12.

2. 1/d-7 factor the d^2-49 to (d+7)(d-7). cancel out the (d+7)

3. (t-5)/(t-4) factor both numerator and denominator. so then it's: (t-5)(t+5)/(t+5)(t-4) cancel out the (t+5)'s

4. (x+2)/(2x-8) factor out a 2 from the numerator and factor out a 4 from the denominator. [2(x^2+3x+2)]/[4(x^2-3x-4)] then factor the polynomial expressions. so then you should have [2(x+2)(x+1)]/[4(x-4)(x+1)]. cancel out the (x+1). reduce the coefficients 2 and 4. then re-distribute the 2 in the denominator.

5. -1/(y+4) factor out a -1 from the numerator. factor the denominator. you should have -[(y-6)/(y-6)(y+4)] cancel out the (y-6).

1. To solve 1.4x12 / 4x, you can simplify the expression by canceling out the factors that appear in both the numerator and the denominator. In this case, the factor "4x" appears in both the numerator and denominator, so it can be canceled out.

The expression simplifies to: 1.4x12 / 4x = 12.

2. For the expression d+7 / d^2-49, you can simplify it by factoring the denominator. The denominator can be factored using the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, the denominator d^2 - 49 is a difference of squares, where a = d and b = 7. Therefore, you can factor it as (d + 7)(d - 7).

Now, let's simplify the expression by canceling out the common factor "d + 7" in the numerator and denominator.

The expression simplifies to: (d + 7) / (d + 7)(d - 7) = 1 / (d - 7).

3. To simplify the expression t^2-25 / t^2+t-20, you can factor both the numerator and denominator. This allows you to identify common factors and cancel them out.

The numerator t^2 - 25 is a difference of squares and can be factored as (t + 5)(t - 5).

The denominator t^2 + t - 20 can be factored as (t + 5)(t - 4).

Now, cancel out the common factor "t + 5" in the numerator and denominator.

The expression simplifies to: (t - 5) / (t - 4).

4. For the expression 2x^2+6x+4 / 4x^2-12x-16, you can simplify it by factoring both the numerator and denominator.

The numerator 2x^2 + 6x + 4 can be factored by grouping: (2x + 2)(x + 2).

The denominator 4x^2 - 12x - 16 can be factored by factoring out a common factor of 4: 4(x^2 - 3x - 4). Then, factor the quadratic expression inside the parentheses: 4(x - 4)(x + 1).

Now, cancel out the common factors "(x + 2)" and "(x + 1)" in the numerator and denominator.

The expression simplifies to: (2x + 2) / 4(x - 4).

You can further simplify by reducing the coefficients: (2/4)(x + 1) / (x - 4) = (1/2)(x + 1) / (x - 4).

5. To simplify the expression 6-y / y^2-2y-24, you can factor both the numerator and denominator.

The numerator 6 - y can be rewritten as -1(y - 6).

The denominator y^2 - 2y - 24 can be factored as (y - 6)(y + 4).

Now, cancel out the common factor "y - 6" in the numerator and denominator.

The expression simplifies to: -1 / (y + 4).