Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem asks us to prove that the solution of the equation $\frac{3m}{9m^2 - 12mx + 4x^2} - \fra...

EquationsAlgebraic ManipulationRational Expressions

The problem is to solve the equation $M = \frac{n(v+w)}{v-w}$ for $v$. $M$, $n$, and $w$ are real nu...

Equation SolvingAlgebraic ManipulationLinear EquationsVariable Isolation

The problem asks to solve the equation $3v = h^2(3r - h)$ for $r$, where $v$ and $h$ are real number...

Equation SolvingVariable IsolationAlgebraic Manipulation

We need to solve the equation $\frac{x-1}{a-3} - \frac{ax}{a^2+3a+9} = \frac{21x-a^2}{a^3-27}$ for $...

EquationsAlgebraic ManipulationFactoringSolving for x

We are given the following equation and asked to solve for $x$: $$ \frac{3}{x-m} - \frac{2}{x+m} = \...

EquationsRational ExpressionsSolving Equations

Solve the equation $(2x - 3b)^2 = (x + 6b)(x - 9b)(8x - 12b) - (3b)^3$ for $x$.

Cubic EquationsPolynomial EquationsVariable Substitution

We are asked to solve several equations. Let's solve problem 71. a). The equation is $(3y - 2c)^2 - ...

EquationsSimplificationVariablesSolutionsExpansion

The problem asks us to solve for $x$ in the following equation: $(2x - 3b)^2 = (x + 6b)(x - 9b)(8x -...

EquationsPolynomial EquationsVariable SubstitutionSimplification

We need to solve for $x$ in the following four equations, where $m$ is a real parameter: a) $m(mx + ...

Linear EquationsQuadratic EquationsParameterSolving Equations

We are asked to solve the following equations for $x$, where $a$ is a real parameter: a) $1 - 3a + 5...

Linear EquationsQuadratic EquationsSolving EquationsParameter

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