Сократить дробь. 10x^2 + 5xy _________ 4x^2 - y^2

В числителе: 5Х (2Х+У)
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5х_____2х-у (наверное)

Help me solve each system by the substitution method:
y=x^2-4x-10
y=-x^2-2x+14
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These are quadratics (2nd order eqns). I don't think substution applies.
y=x^2-4x-10
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax^2+bx+c=0 (in our case 1x^2+-4x+-10+=+0) has the following solutons:

x[12]+=+(b+-sqrt(+b^2-4ac+))/2\a

For these solutions to exist, the discriminant b^2-4ac should not be a negative number.

First, we need to compute the discriminant b^2-4ac: b^2-4ac=(-4)^2-4*1*-10=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x[12]+=+(--4+-sqrt(+56+))/2\a.

x[1]+=+(-(-4)+sqrt(+56+))/2\1+=+5.74165738677394
x[2]+=+(-(-4)-sqrt(+56+))/2\1+=+-1.74165738677394

Quadratic expression 1x^2+-4x+-10 can be factored:
1x^2+-4x+-10+=+(x-5.74165738677394)*(x--1.74165738677394)
Again, the answer is: 5.74165738677394, -1.74165738677394. Here's your graph:
graph(+500,+500,+-10,+10,+-20,+20,+1*x^2+-4*x+-10+)

It's

2 + sqrt(14)
2 - sqrt(14)
----------------
y=-x^2-2x+14
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax^2+bx+c=0 (in our case 1x^2+-2x+14+=+0) has the following solutons:

x[12]+=+(b+-sqrt(+b^2-4ac+))/2\a

For these solutions to exist, the discriminant b^2-4ac should not be a negative number.

First, we need to compute the discriminant b^2-4ac: b^2-4ac=(-2)^2-4*1*14=-52.

The discriminant -52 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -52 is + or - sqrt(+52)+=+7.21110255092798.

The solution is x[12]+=+(--2+-i*sqrt(+-52+))/2\1+=++(--2+-i*7.21110255092798)/2\1+, or
Here's your graph:
graph(+500,+500,+-10,+10,+-20,+20,+1*x^2+-2*x+14+)

This one is:
1 + sqrt(-13)
1 - sqrt(-13)

New! FREE algebra s
или так

x = -(-4) divided by 2(-2)
x = 4 divided by -4
x = -1

now plug it in
f(x) = -2(-1) - 4(-1) - 10
y = 2 +4 - 10
y = -4

The vertex is (-1, -4)