Question about rearranging complex formula?

Hello:

Given: a = (2 - 7b) / (b - 5), this is a fraction function which expresses ' a ' with respect to ' b '.

To make ' b ' the subject of the formula, in other words is to express ' b ' with respect to ' a ',

>>> First Step:

Apply the cross-multiplication process, which says that if you have the following equality:

(a / b) = (c / d) it gives (a * d) = (b * c)

So, applying this formula on your case, you will get:

a = (2 - 7b) / (b - 5) gives (a / 1) = (2 - 7b) / (b - 5) [ Note: I divide ' a ' by 1 for clarification and that do not affect the equation ]

Thus, by cross-multiplication, u will get this: ( a )*( b - 5) = ( 1 )*(2 - 7b)

>>> Second Step:

Simplify the equation using the formula: " a*( b - c ) = a*b - a*c " and u will get:

ab - 5a = 2 - 7b

>>> Third Step:

Now, shift the ' 7b ' to the left side of the equation while you change its sign from negative to positive; Also shift the ' 5a ' to the right side of the equation while you change its sign from negative to positive; You will get this:

ab + 7b = 2 + 5a

>>> Fourth Step:

On the left side of the equation take ' b ' as a common factor of ' ab + 7b ' to get:

b*( a + 7) = 2 + 5a

>>> Finally:

To solve for ' b ', divide both sides of the equation by the quantity ' (a + 7) ' to keep ' b ' alone on the left side and you will get:

[b*( a + 7)] / (a + 7) = (2 + 5a) / (a + 7)

Now cancel the (a + 7) with the (a + 7) on the left side of the equation to get the final answer:

b = (2 + 5a) / (a + 7)

a=(2-7b)/(b-5)

=> a(b-5)=(2-7b)

=> ab-5a=2-7b

=> ab+7b=2+7

=> b(a+7)=5

=> b = 5/(a+7) <============= Answer.

a = (2 – 7b)/(b – 5)

a(b – 5) = 2 – 7b

ab – 5a = 2 – 7b

ab + 7b = 5a + 2

b(a + 7) = 5a + 2)

b = (5a + 2)/(a + 7)

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the reason maximum individuals locate this no longer straightforward is as a results of the fact x seems two times interior the formulation, and how around this is constantly to factorise at some point interior the working. y = 4x / (x+2) Multiply the two factors via x+2: y(x+2) = 4x Multiply out the brackets: yx + 2y = 4x Re-set up so the xs are all on the comparable facet: 2y = 4x - yx Factorise: 2y = x(4-y) Divide via 4-y: 2y/(4-y) = x x = 2y/(4-y) i'm hoping this enables.

a = (2 - 7b)/(b - 5)

a(b - 5) = 2 - 7b

ab - 5a = 2 - 7b

-5a - 2 = -7b - ab

-5a - 2 = b(-7 - a)

b = (-5a - 2)/(-7 - a)

b = (5a + 2)/(a + 7)

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