Help identifying missing part of algebra education

I am unable to follow an explanation provided in 'Mathematical Fundamentals: The Quadratic Formula' and was wondering if anyone could point me in the right direction so that I can fill in the necessary gap(s) in my algebra education?

Problem referenced: https://brilliant.org/practice/quadratic-formula/?p=9

In the explanation provided to the above referenced problem I'm confounded straight out of the gate; I don't understand why you would/should 'multiply a by the denominator and numerator so that it has the same denominator as the term it is subtracting from' - I see that doing this makes both denominators the same, however don't understand why doing this is okay.

Any help greatly appreciated, Matthew

#Algebra

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Comments

You're basically subtracting two fractions.

$\frac45 - \frac23 = \frac{4\times3 - 2\times5}{5\times3}$

So $\dfrac{b^2}{a^2} - \dfrac{4c}a = \dfrac{b^2 \times a - 4c \times a^2}{a\times a^3} = \dfrac{a \times b^2 - a \times 4c \times a}{a \times a^2} = \dfrac{\cancel a( b^2 - 4c \times a)}{\cancel a \times a^2} = \dfrac{ b^2 - 4c \times a}{ a^2}$

Pi Han Goh - 11 months, 2 weeks ago

Thanks Pi! Very kind of you and just what I needed 🙏🏼

Matt Lee - 11 months, 1 week ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$