Can anyone explain to me how to work out these type of equations simply please?

Question

one is
solve the following equation to find x in terms of a and b, assuming that a can not equal b.
i know the answer to this is x = -a-b but how do you get to that.
the other is
x in terms of y and t, assuming that y+3t can not equal 0.
i have attempted this one and worked it out to be x= 3t - y. but am still not sure how to solve them.
if you could explain very simply and clearly to me how you solve these that would be great as i am having problems understanding what to do.
thank you for any help you can give.

the first one is
a(x+a) = b(x+b)
and the second is
y(y - x) = 3t(3t+x)
sorry about that

Answer 1

Where are the problems themselves??

The idea is to isolate the x-values. So in a(x+a) = b(x+b) first expand: ax + a^2 = bx + b^2. Now group the x-terms: ax-bx = b^2 - a^2, and x(a-b) = b^2-a^2, and x = (b^2-a^2)/(a-b) = (b-a)/(b+a)/(a-b) = -(b+a) = -a-b

Similarly, y(y-x) = 3t(3t+x). First expand: y^2 - yx = 9t^2 + 3tx. Group x-terms: 3tx + yx = y^2 - 9t^2, and x(3t+y) = (y+3t)(y-3t), so x = y-3t. I think you missed a - sign somewhere.

Answer 2

Question 1
a (x + a) = b(x + b)
a x + a ² = b x + b ²
ax - bx = b² - a²
(a - b) x = (b - a) (b + a)
(a - b) x = - (a - b) (b + a)
x = - (b + a)

Question 2
y ² - x y = 9t² + 3tx
y ² - 9 t ² = 3 t x + x y
y ² - 9 t² = (3 t + y) x
x = (y ² - 9 t ²) / (3 t + y)
x = (y - 3 t) (y + 3 t) / (y + 3 t)
x = y - 3 t

Answer 3

ur question is
a(x+a)=b(x+b)
multiply
we get
ax+a2=bx+b2(a2 is nothing but a square ie a2=a*a)
bring bx to left hand side&take a2 to right hand side
then we get
x(a-b)=b2-a2
we know a formula i.e b2=a2=(b-a)(b+a)..........formula (1)
therefore
x(a-b)=(b-a)(b+a)
on taking minus common
x(a-b)=-(a-b)(a+b)
since u said a is not equal to b cance (a-b) on both sides
we get x=-(a+b)
x=-a-b

next equation is
y(y-x)=3t(3t+x)
multipling
y2-xy=9t2+3tx
bring 9t2 to left hand side&take xy to right hand side
y2-9t2=3tx+xy
taking x common on right hand side&using formula (1) on left hand side
(y-3t)(y+3t)=x(3t+y)
since u said y+3t not equal to zero cancel (y+3t) on both sides
then we get
y-3t=x
hence the answer is x=y-3t

Answer 4

and whats the equation??