Solving Equations and Fractions

The video tutorial explains how to solve equations for a specific variable, focusing on two examples. The first example involves solving for 'a' in the equation b = h/a by eliminating the fraction and using cross multiplication. The second example demonstrates solving for 'a' in the quadratic equation ax^2 - BX - C = 0 by isolating terms and expressing the solution in different forms. The tutorial highlights multiple methods and simplifications to achieve the solution.

What is the main challenge when solving the equation b = h / a for a?

• a is in the numerator

• b is a constant

• a is in the denominator

• h is unknown

How can we eliminate the fraction in the equation b = h / a?

• Add a to both sides

• Subtract a from both sides

• Multiply both sides by a

• Divide both sides by a

What is the result of multiplying both sides of b = h / a by a?

• a * b = h

• b = a / h

• a = h * b

• h = a * b

Which method can be used as an alternative to solve b = h / a?

• Cross-multiplication

• Substitution

• Elimination

• Graphing

What is the equation obtained after cross-multiplying b = h / a?

• h / a = b

• a * b = 1 * h

• a / b = h

• b * h = a

In the equation ax^2 - BX - C = 0, what is the first step to solve for a?

• Divide both sides by x^2

• Multiply both sides by x^2

• Subtract BX and C from both sides

• Add BX and C to both sides

What is the purpose of adding BX and C to both sides in ax^2 - BX - C = 0?

• To solve for x

• To simplify the equation

• To isolate ax^2

• To eliminate x^2

After isolating ax^2, what is the next step to solve for a?

• Divide both sides by x^2

• Add x^2 to both sides

• Subtract x^2 from both sides

• Multiply both sides by x^2

How can the solution a = (BX + C) / x^2 be expressed differently?

• As a single fraction

• As two separate fractions

• As a sum of products

• As a product of fractions

What is the simplified form of a = BX / x^2 + C / x^2?

• a = B / x + C / x^2

• a = Bx + Cx^2

• a = Bx^2 + Cx

• a = B / x^2 + C / x