As from a formula to express a variable

As from a formula to express a variable

The concept "formula" is rather widely used not only in the exact sciences, but in relation to mathematics by this word most often designate some identity. It is record of two sequences of the mathematical operations applied to one or several variables between which there is an equal-sign. To express one variable of identity through all others, it is necessary to transform this equality so that in the left part there was only this variable.


1. Begin transformations, for example, with disposal of fractions if they are in an initial formula. For this purpose increase both parts of equality by a common denominator. For example, formula 3*Y = √X/2 after this step has to take a form 6*Y = √X.

2. If expression contains a root of any degree in one part of equality, then get rid also of it, having built both parts of identity in the degree equal to a root indicator. For the example given above this action has to be expressed in transformation of a formula to such look: 36*Y² = X. Sometimes it is more convenient to make operation of this step before action from a step previous.

3. Transform expression so that all members of identity containing the necessary variable appeared in the left part of equality. For example, if the formula has an appearance 36*Y-X*Y+5=X and you are interested in variable X, will be to trade places the left and right half of identity enough. And if it is necessary to express Y, then the formula as a result of this action has to take a form 36*Y-X*Y=X-5.

4. Simplify expression in the left part of a formula so that the required variable became one of factors. For example, for a formula from the previous step it can be done so: Y * (36-X) = X-5.

5. Divide expressions on both sides of an equal-sign into factors of the variable interesting you. As a result in the left part of identity there has to be only this variable. The example used above after this step would take such form: Y = (X-5)/(36-X).

6. If the required variable as a result of all transformations is built in what in degree, then get rid of degree extraction of a root from both parts of a formula. For example, the formula from the second step to this stage of transformations has to come trudging a type of Y²=X/36. And its final look has to become such: Y= √ X/6.

Author: «MirrorInfo» Dream Team