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Simplifying Rational Algebraic Expressions​

Simplifying Rational Algebraic Expressions class=

Sagot :

MindOverMatteridn

✏Simplifying Rational Algebraic Expressions

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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]

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