Notice that the bottom part is 3^2 - y^2 = (3 + y)(3 - y). Also, that 2 next to y^2 on the top part is annoying, so I will divide the top and the bottom by 2: Taking these two things into account, we have:
y^2 - 8y + 15
____________ Now the top is easy to factorize:
(3 + y)(3 - y)
_____
2
(y - 5)(y - 3)
____________ Now I'm going to multiply the top and the bottom by 2 to get rid of the bottom 2:
(3 + y)(3 - y)
____
2
2*(y - 5)(y - 3)
____________
(3 + y)(3 - y)
Now look here: we need to change that (y - 3) on top to (3 - y) so that it matches the bottom expression and cancel it out. There are many ways of looking at this, but the fact is that the expression (y - 5) will also change to (5 - y). You can say that to justify the switches you are multiplying the top half by (-1) twice because (-1) times (-1) equals +1 and that way you aren't changing the sign of the equation. You might have other ways of seeing it. So we get:
2*(5 - y)(3 - y)
____________ Finally, cancelling, we get:
(3 + y)(3 - y)
2*(5 - y)
_______
(3 + y)
That's as simplified as it gets. Choose any number for "y" in the first way the problem was expressed and notice that you will get the same result in the simplified expression. I hope this helps...
First, keep in mind your order of operations: Parentheses, Exponents, Multiplication, branch, Addition Subtraction Now multiply out the parenthesis on the two sides of the equation: (2x+3) X (x-4) = (x-4) X (3x+7) in case you be conscious, the two those sides of the equation are elevated via (x-4) so which you would be able to purely ingredient out that factor era. Its the comparable as in case you divided via (x-4) and because you do it to the two sides its completely ok. Now you're left with (2x+3) = (3x+7) you could now purely combine the like words and isolate the variable. to try this subtract 2x from the two sides, this might pass away 0x (which you would be able to pass away out) on th left component and 1x (or purely x) interior the outstanding component. 3=x+7 Do the comparable element for the first numbers and subtract 7 from the two sides. You get -4 on the left component and not something on the outstanding component. you're actually left with -4=x, that's the comparable as x=-4. And thats your answer desire that helps!
Comments
2y^(2)-16y+30
____________
9-y^(2)
Notice that the bottom part is 3^2 - y^2 = (3 + y)(3 - y). Also, that 2 next to y^2 on the top part is annoying, so I will divide the top and the bottom by 2: Taking these two things into account, we have:
y^2 - 8y + 15
____________ Now the top is easy to factorize:
(3 + y)(3 - y)
_____
2
(y - 5)(y - 3)
____________ Now I'm going to multiply the top and the bottom by 2 to get rid of the bottom 2:
(3 + y)(3 - y)
____
2
2*(y - 5)(y - 3)
____________
(3 + y)(3 - y)
Now look here: we need to change that (y - 3) on top to (3 - y) so that it matches the bottom expression and cancel it out. There are many ways of looking at this, but the fact is that the expression (y - 5) will also change to (5 - y). You can say that to justify the switches you are multiplying the top half by (-1) twice because (-1) times (-1) equals +1 and that way you aren't changing the sign of the equation. You might have other ways of seeing it. So we get:
2*(5 - y)(3 - y)
____________ Finally, cancelling, we get:
(3 + y)(3 - y)
2*(5 - y)
_______
(3 + y)
That's as simplified as it gets. Choose any number for "y" in the first way the problem was expressed and notice that you will get the same result in the simplified expression. I hope this helps...
First, keep in mind your order of operations: Parentheses, Exponents, Multiplication, branch, Addition Subtraction Now multiply out the parenthesis on the two sides of the equation: (2x+3) X (x-4) = (x-4) X (3x+7) in case you be conscious, the two those sides of the equation are elevated via (x-4) so which you would be able to purely ingredient out that factor era. Its the comparable as in case you divided via (x-4) and because you do it to the two sides its completely ok. Now you're left with (2x+3) = (3x+7) you could now purely combine the like words and isolate the variable. to try this subtract 2x from the two sides, this might pass away 0x (which you would be able to pass away out) on th left component and 1x (or purely x) interior the outstanding component. 3=x+7 Do the comparable element for the first numbers and subtract 7 from the two sides. You get -4 on the left component and not something on the outstanding component. you're actually left with -4=x, that's the comparable as x=-4. And thats your answer
desire that helps!