Correct way to refer to solve an equation

I am a mathematician and I have a question about how to say correctly in English the next preceding:

Let x=(...)(,,,)
If we clear away the first parenthesis we get:
(...)=x/(,,,,)

The “clear away” is good for this situation? Thanks.

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You have "divided through" by the second bracket. This is an aspect of "rearranging" the equation, usually done to change the subject of the equation.

Such a process would normally be described this way in school maths, but in research maths, it would probably not even be commented on. The assumption is that a professional mathematician would be able to follow the algebra without needing it each step explained to her.

I think the term for what you are doing with the first parenthesis is "isolate". An example (very basic math) of how this word is used can be found here.

For example

x = f(x,y)*g(x,y)

we can isolate f(x,y) by dividing both sides by g(x,y), which would yield

f(x,y) = x/g(x,y)

If f(x,y) (the expression you isolated) is your desired answer, this would be solving for f(x,y) by isolating it from the other terms.

Suitable Phrases

• to carry over

The denominator was carried over to solve the equation

x / 2 = 3 x = 2 × 3 x = 6

• to rearrange

The equation for velocity was rearranged to find the distance travelled given the time and velocity

v = d/t d = v × t

• to make [something] the subject

He made p the subject since he knew the value of q.

q = 5 q = 10 - p p = 10 + q p = 10 + 5 = 15

• to change the subject

The answer became clear only after she changed the subject of the equation.

• to solve for [something]

He solved for x first before solving for y in the simultaneous equations.

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