Math Problem Statement

Solve the equation: (4k^2 - 3k - 1) / (4k^2 + 11k + 7) = (16k^2 - 1) / (4k^2 + 3k - 7)

Solution

The equation in the image is:

4k2−3k−14k2+11k+7=16k2−14k2+3k−7\frac{4k^2 - 3k - 1}{4k^2 + 11k + 7} = \frac{16k^2 - 1}{4k^2 + 3k - 7}

We can solve this by cross-multiplying and simplifying the equation.

Let me start by breaking down each term and proceed step-by-step.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Equations
Cross Multiplication
Factoring

Formulas

Quadratic equation formula ax^2 + bx + c = 0
Cross multiplication: a/b = c/d implies a*d = b*c

Theorems

Fundamental Theorem of Algebra
Factoring Quadratic Equations

Suitable Grade Level

Grades 9-11

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