Simplify the expression (3a^2+4ab+b^2)/(4a^2+3ab-b^2)

FEATURES

TOPICS: LINEAR EQUATIONS and QUADRATIC EQUATIONS
LEVEL: FORM 3
SOURCE: KCSE 2000 PAPER 1, QUESTION 2
MARKS: 3

SOLUTION

To simplify the expression $\frac{3a^2 + 4ab + b^2}{4a^2 + 3ab - b^2}$ , we follow these steps:

Step 1: Factor the Numerator and Denominator

Numerator: $3a^2 + 4ab + b^2$

We can rewrite it as:

$3a^2 + 4ab + b^2 = (3a + b)(a + b)$

Denominator: $4a^2 + 3ab - b^2$

We can rewrite it as:

$4a^2 + 3ab - b^2 = (4a - b)(a + b)$

Step 2: Rewrite the Expression

Now we have:

$\frac{(3a + b)(a + b)}{(4a - b)(a + b)}$

Step 3: Cancel Common Factors

Canceling $a + b$ gives us:

$\frac{3a + b}{4a - b}$

Final Result

The simplified form is:

$\frac{3a + b}{4a - b}$

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Simplify the expression (3a^2+4ab+b^2)/(4a^2+3ab-b^2)

FEATURES

SOLUTION