✏Simplifying Rational Algebraic Expressions
===================================
Answer:
1. [tex]\bold{ \frac{2}{3} }[/tex]
2.[tex]\bold{ \frac{x}{2} }[/tex]
3. [tex]\bold{ \frac{v + 7}{2}} [/tex]
4.[tex]\bold{ \frac{x + 7}{x + 6}} [/tex]
Step-by-step explanation:
1. Find the GCD or HCF of numerator and denominator Divide Both numerator and denominator by the GCD:
GCD:8
- [tex] \frac{16 \div 8}{24 \div 8} = \boxed{\bold{\frac{2}{3} }}[/tex]
2. Simplify and Reduce
- [tex] \frac{ {14x}^{2} }{28x} [/tex]
- Simplify the expression:
- [tex] \frac{ 14 \:{x}^{ \cancel2} }{28 \cancel{x}} = \frac{14x}{28} = \boxed{ \bold{ \frac{x}{2} }}[/tex]
3. Factor the expressions:
- [tex] \frac{ {v - 49}^{2} }{2v - 14} = \frac{(v - 7) \times (v + 7)}{2(v + 7)} [/tex]
- Reduce the Fraction:
- [tex] \boxed{ \bold{ \frac{v + 7}{2} }}[/tex]
4. Rewrite
- [tex] \frac{ {x}^{2} + 7x - 6x - 42}{(x - 6) \times (x + 6)} [/tex]
- Factor The expressions:
- [tex] \frac{x(x + 7) - 6(x + 7)}{(x - 6) \times (x + 6)} [/tex]
- Factor the expressions:
- [tex] \frac{(x + 7)(x - 6)}{(x - 6)(x + 6)} [/tex]
- Reduce the Fraction:
- [tex] \frac{(x + 7) \cancel{(x - 6)}}{ \cancel{(x - 6)}(x + 6)} = \boxed{ \bold{ \frac{x + 7}{x + 6} }}[/tex]
#CarryOnLearning
===================================
